Transcript Introduction to Quantum Mechanic

Complex hardware systems
based on quantum optics
1
Basics of Quantum Mechanics
- Why Quantum Physics? • Classical mechanics (Newton's mechanics) and
Maxwell's equations (electromagnetics theory) can
explain MACROSCOPIC phenomena such as motion of
billiard balls or rockets.
• Quantum mechanics is used to explain microscopic
phenomena such as photon-atom scattering and flow of
the electrons in a semiconductor.
• QUANTUM MECHANICS is a collection of postulates
based on a huge number of experimental observations.
• The differences between the classical and quantum
mechanics can be understood by examining both
– The classical point of view
– The quantum point of view
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Basics of Quantum Mechanics
- Quantum Point of View • Quantum particles can act as both particles and waves
 WAVE-PARTICLE DUALITY
• Quantum state is a conglomeration of several possible
outcomes of measurement of physical properties 
Quantum mechanics uses the language of
PROBABILITY theory (random chance)
• An observer cannot observe a microscopic system
without altering some of its properties. Neither one can
predict how the state of the system will change.
• QUANTIZATION of energy is yet another property of
"microscopic" particles.
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Christiaan Huygens
Dutch 1629-1695
light consists of waves
The idea of duality is
rooted in a debate
over the nature of
light and matter
dating back to the
1600s, when
competing theories
of light were
proposed by
Huygens and
Newton.
Sir Isaac Newton
1643 1727
light consists of particles
4
If h is the Planck constant
Then
Louis de BROGLIE
French
(1892-1987)
Max Planck (1901)
Göttingen
5
Soon after the
electron discovery in 1887
- J. J. Thomson (1887) Some negative
part could be extracted from the atoms
- Robert Millikan (1910) showed that it was
quantified.
-Rutherford (1911) showed that the negative part
was diffuse while the positive part was concentrated.
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Quantum numbers
In mathematics, a natural
number (also called counting
number)
has
two
main
purposes: they can be used for
counting ("there are 6 apples on
the table"), and they can be
used for ordering ("this is the
3rd largest city in the country").
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Atomic Spectroscopy
Absorption or Emission
Johannes Rydberg 1888
Swedish
n1 → n2
name
Converges
to (nm)
1 → ∞
Lyman
91
2 → ∞
Balmer
365
3→ ∞
Pashen
821
4 → ∞
Brackett
1459
5 → ∞
Pfund
2280
6→ ∞
Humphreys
3283
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Bohr and Quantum
Mechanical Model
Wavelengths and energy
• Understand that different wavelengths of
electromagnetic radiation have different
energies.
• c=vλ
– c=velocity of wave
– v=(nu) frequency of wave
– λ=(lambda) wavelength
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• Bohr also postulated that an atom
would not emit radiation while it was
in one of its stable states but rather
only when it made a transition
between states.
• The frequency of the radiation
emitted would be equal to the
difference in energy between those
states divided by Planck's constant.
10
E2-E1= hv
h=6.626 x 10-34 Js = Plank’s constant
E= energy of the emitted light (photon)
v = frequency of the photon of light
• This results in a unique emission spectra for each
element, like a fingerprint.
• electron could "jump" from one allowed energy state
to another by absorbing/emitting photons of radiant
energy of certain specific frequencies.
• Energy must then be absorbed in order to "jump" to
another energy state, and similarly, energy must be
emitted to "jump" to a lower state.
• The frequency, v, of this radiant energy corresponds
exactly to the energy difference between the two
states.
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• In the Bohr model, the electron is in a
defined orbit
• Schrödinger model uses probability
distributions for a given energy level of the
electron.
Orbitals and quantum
numbers
• Solving Schrödinger's equation leads to
wave functions called orbitals
• They have a characteristic energy and
shape (distribution).
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• The lowest energy orbital of the hydrogen
atom has an energy of -2.18 x 1018 J and the
shape in the above figure. Note that in the
Bohr model we had the same energy for the
electron in the ground state, but that it was
described as being in a defined orbit.
• The Bohr model used a single
quantum number (n) to describe
an orbit, the Schrödinger model
uses three quantum numbers: n, l
and ml to describe an orbital
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The principle quantum
number 'n'
• Has integral values of 1, 2, 3, etc.
• As n increases the electron density is
further away from the nucleus
• As n increases the electron has a higher
energy and is less tightly bound to the
nucleus
14
The azimuthal or orbital
(second) quantum number
'l'
• Has integral values from 0 to (n-1) for
each value of n
• Instead of being listed as a numerical
value, typically 'l' is referred to by a letter
('s'=0, 'p'=1, 'd'=2, 'f'=3)
• Defines the shape of the orbital
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The magnetic (third) quantum
number 'ml'
Has integral values between 'l' and -'l', including 0
Describes the orientation of the orbital in space
For example, the electron orbitals with
a principle quantum number of 3
n
l
Subshell
ml
Number of
orbitals in
subshell
1
3
3
0
1
3s
3p
0
-1,0,+1
2
3d
-2,1,0,+1,+2 5
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• the third electron shell (i.e. 'n'=3) consists
of the 3s, 3p and 3d subshells (each with a
different shape)
• The 3s subshell contains 1 orbital, the 3p
subshell contains 3 orbitals and the 3d
subshell contains 5 orbitals. (within each
subshell, the different orbitals have different
orientations in space)
• Thus, the third electron shell is comprised
of nine distinctly different orbitals,
although each orbital has the same energy
(that associated with the third electron shell)
Note: remember, this is for hydrogen only.
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Subshell
Number of orbitals
s
1
p
3
d
5
f
7
18
19
Practice:
• What are the possible values of l and
ml for an electron with the principle
quantum number n=4?
• If l=0, ml=0
• If l=1, ml= -1, 0, +1
• If l=2, ml= -2,-1,0,+1, +2
• If l=3, ml= -3, -2, -1, 0, +1, +2, +3
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Problem #2
• Can an electron have the quantum
numbers n=2, l=2 and ml=2?
• No, because l cannot be greater than n-1,
so l may only be 0 or 1.
• ml cannot be 2 either because it can never
be greater than l
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In order to explain the line spectrum of hydrogen, Bohr made one
more addition to his model. He assumed that the electron could
"jump" from one allowed energy state to another by
absorbing/emitting photons of radiant energy of certain specific
frequencies. Energy must then be absorbed in order to "jump"
to another energy state, and similarly, energy must be emitted
to "jump" to a lower state. The frequency, v, of this radiant
energy corresponds exactly to the energy difference between
the two states. Therefore, if an electron "jumps" from an initial
state with energy Ei to a final state of energy Ef, then the
following equality will hold:
(delta) E = Ef - E i = hv
To sum it up, what Bohr's model of the hydrogen atom states is
that only the specific frequencies of light that satisfy the above
equation can be absorbed or emitted by the atom.
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Atomic Spectroscopy
Absorption or Emission
-R/72
-R/62
-R/52
-R/42
Johannes Rydberg 1888
Swedish
-R/32
IR
-R/22
VISIBLE
-R/12
UV
Emission
Quantum numbers n, levels are not equally spaced
R = 13.6 eV
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Photoelectric Effect (1887-1905)
discovered by Hertz in 1887 and explained in 1905 by Einstein.
I
Albert EINSTEIN
(1879-1955)
Heinrich HERTZ
(1857-1894)
Vacuum
Vide
e
i
e
e
24
I
T (énergie
cinétique)
Kinetic energy

0

0
25
Compton effect 1923
playing billiards assuming l=h/p
h '
h

h/ l
h/ l'

2
p /2m
p
Arthur Holly Compton
American
1892-1962
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Davisson and Germer 1925

d
Clinton Davisson
Lester Germer
In 1927
2d sin
 = k l
Diffraction is similarly observed using a monoenergetic electron beam
Bragg law is verified assuming l=h/p
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Wave-particle Equivalence.
•Compton Effect (1923)
•Electron Diffraction Davisson and Germer (1925)
•Young's Double Slit Experiment
Wave–particle duality
In physics and chemistry, wave–particle duality is the
concept that all matter and energy exhibits both wave-like
and particle-like properties. A central concept of quantum
mechanics, duality, addresses the inadequacy of classical
concepts like "particle" and "wave" in fully describing the
behavior of small-scale objects. Various interpretations of
quantum mechanics attempt to explain this apparent
paradox.
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Young's Double Slit Experiment
F1
Source
F2
Ecranwith
Mask
2 slits
Screen photo
Plaque
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Young's Double Slit Experiment
This is a typical experiment showing the wave nature of
light and interferences.
What happens when we decrease the light intensity ?
If radiation = particles, individual photons reach one
spot and there will be no interferences
If radiation  particles there will be no spots on the
screen
The result is ambiguous
There are spots
The superposition of all the impacts make interferences
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Young's Double Slit Experiment
Assuming a single electron each time
What means interference with itself ?
What is its trajectory?
If it goes through F1, it should ignore the presence of F2
F1
Source
F2
Mask
Ecran
Plaque photo
Screen
with 2
slits
31
Young's Double Slit Experiment
There is no possibility of knowing through which split the photon went!
If we measure the crossing through F1, we have to place a screen behind.
Then it does not go to the final screen.
We know that it goes through F1 but we do not know where it would go after.
These two questions are not compatible
Two important differences with
classical physics:
F1
Source
F2
• measurement is not independent
from observer
• trajectories are not defined; h goes
through F1 and F2 both! or through
them with equal probabilities!
Mask
Ecran
Plaque photo
Screen
with 2
slits
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de Broglie relation from relativity
Popular expressions of relativity:
m0 is the mass at rest, m in motion
E like to express E(m) as E(p) with p=mv
Ei + T + Erelativistic + ….
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de Broglie relation from relativity
Application to a photon (m0=0)
To remember
To remember
34
Useful to remember to relate energy
and wavelength
Max Planck
35
A New mathematical tool:
Wave functions and Operators
Each particle may be described by a wave function Y(x,y,z,t), real or complex,
having a single value when position (x,y,z) and time (t) are defined.
If it is not time-dependent, it is called stationary.
The expression Y=Aei(pr-Et) does not represent one molecule but a flow of
particles: a plane wave
36
Wave functions describing one particle
To represent a single particle Y(x,y,z) that does not evolve in time, Y(x,y,z) must
be finite (0 at ∞).
In QM, a particle is not localized but has a probability to be in a given volume:
dP= Y* Y dV is the probability of finding the particle in the volume dV.
Around one point in space, the density of probability is dP/dV= Y* Y
Y has the dimension of L-1/3
Integration in the whole space should give one
Y is said to be normalized.
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Normalization
An eigenfunction remains an eigenfunction
when multiplied by a constant
O(lY)= o(lY) thus it is always possible to
normalize a finite function
Dirac notations
<YIY>
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Mean value
• If Y1 and Y2 are associated with the same
eigenvalue o: O(aY1 +bY2)=o(aY1 +bY2)
• If not O(aY1 +bY2)=o1(aY1 )+o2(bY2)
we define ō = (a2o1+b2o2)/(a2+b2)
Dirac notations
39
Introducing new variables
Now it is time to give a physical meaning.
p is the momentum, E is the Energy
H=6.62 10-34 J.s
40
Plane waves
This represents a (monochromatic) beam, a
continuous flow of particles with the same
velocity (monokinetic).
k, l,w, , p and E are perfectly defined
R (position) and t (time) are not defined.
YY*=A2=constant everywhere; there is no
localization.
If E=constant, this is a stationary state,
independent of t which is not defined.
41
Correspondence principle 1913/1920
For every physical quantity
one can define an operator.
The definition uses
formulae from classical
physics replacing
quantities involved by the
corresponding operators
Niels Henrik David Bohr
Danish
1885-1962
QM is then built from classical physics in spite
of demonstrating its limits
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Operators p and H
We use the expression of the plane wave
which allows defining exactly p and E.
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Momentum and Energy Operators
Remember during this chapter
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Stationary state E=constant
Remember for 3 slides after
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Kinetic energy
Classical
quantum operator
In 3D :
Calling
the laplacian
Pierre Simon, Marquis de Laplace
(1749 -1827)
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Correspondence principle
angular momentum
Classical expression
Quantum expression
lZ= xpy-ypx
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48
49
50
51
Time-dependent Schrödinger Equation
Without potential E = T
With potential E = T + V
Erwin Rudolf Josef Alexander Schrödinger
Austrian
1887 –1961
52
Schrödinger Equation for stationary states
Potential energy
Kinetic energy
Total energy
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Schrödinger Equation for stationary states
Remember
H is the hamiltonian
Half penny bridge in Dublin
Sir William Rowan Hamilton
Irish 1805-1865
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Chemistry is nothing but an application of Schrödinger Equation (Dirac)
< YI Y> <Y IOI Y >
Dirac notations
Paul Adrien Dirac 1902 – 1984
Dirac’s mother was British and his father was Swiss.
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Uncertainty principle
the Heisenberg uncertainty principle states that
locating a particle in a small region of space
makes the momentum of the particle uncertain;
and conversely, that measuring the momentum of
a particle precisely makes the position uncertain
We already have seen incompatible operators
Werner Heisenberg
German
1901-1976
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It is not surprising to find that quantum mechanics does not predict the position
of an electron exactly. Rather, it provides only a probability as to where the
electron will be found.
We shall illustrate the probability aspect in terms of the system of an electron
confined to motion along a line of length L. Quantum mechanical probabilities
are expressed in terms of a distribution function.
For a plane wave, p is defined and the position is not.
With a superposition of plane waves, we introduce an uncertainty on p and we
localize. Since, the sum of 2 wavefucntions is neither an eigenfunction for p nor
x, we have average values.
With a Gaussian function, the localization below is 1/2p
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p and x do not commute and are incompatible
For a plane wave, p is known and x is not (Y*Y=A2 everywhere)
Let’s superpose two waves…
this introduces a delocalization for p and may be localize x
At the origin x=0 and at t=0 we want to increase the total amplitude,
so the two waves Y1 and Y2 are taken in phase
At ± Dx/2 we want to impose them out of phase
The position is therefore known for x ± Dx/2
the waves will have wavelengths
58
Superposition of two waves
2
env eloppe
Y
1
0
-1
4.95
a (radians)
-2
0
1
2
3
Dx/(2x(√2p))
Factor 1/2p a more realistic localization
4
5
Dx/2
59
Uncertainty principle
A more accurate calculation localizes more
(1/2p the width of a gaussian) therefore one gets
Werner Heisenberg
German
1901-1976
x and p or E and t play symmetric roles
in the plane wave expression;
Therefore, there are two main uncertainty principles
60
De Broglie’s postulate: wavelike properties of particles
Matter wave: de Broglie

the total energy of matter related to the frequency ν of the wave is
E=hν

the momentum of matter related to the wavelength λ of the wave is
p=h/λ
Ex: (a) the de Broglie wavelength of a baseball moving at a
speed v=10m/s, and m=1kg. (b) for a electron K=100 eV.
(a) l  h / p  6.6  10
 34
/(1  10)  6.6  10
 35
m  6.6  10
 25
o
A
(b) l  h / p  h / 2mK
 34
 6.6  10 / 2  9.1  10
 l (electron)  l (baseball )
 31
 100  1.6  10
 19
o
 1.2 A
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De Broglie’s postulate: wavelike properties of particles
The experiment of Davisson and Germer
(1) A strong scattered electron beam is detected at θ=50o for V=54 V.
(2) The result can be explained as a constructive interference of waves
scattered by the periodic arrangement of the atoms into planes of the
crystal.
(3) The phenomenon is analogous to the Bragg-reflections (Laue pattern).
 1927, G. P. Thomson showed the diffraction of electron beams passing through
thin films confirmed the de Broglie relation λ=h/p. (Debye-Scherrer method)
62
De Broglie’s postulate: wavelike properties of particles
Bragg reflection:
constructive interference:
2d sin   nl
o
d  0.91 A ,   50o and   90o   / 2  65o
for n  1
o
 l  2d sin   2  0.91  sin 65  1.65 A
o
(X - ray wavelength )
for electron K  54 eV
consistent
 l  h / 2mK
 34
 6.6  10 / 2  9.1  10
(electron wavelength )
 31
 54  1.6  10
19
o
 1.65 A
63
De Broglie’s postulate: wavelike properties of particles
Debye-Scherrer diffraction
X-ray diffraction:
zirconium oxide crystal
electron diffraction :
gold crystal
Laue pattern of X-ray (top) and
neutron (bottom) diffraction for
64
sodium choride crystal
De Broglie’s postulate: wavelike properties of particles
The wave-particle duality
Bohr’s principle of complementarity: The wave and particle models are
complementary; if a measurement proves the wave character of matter, then it
is impossible to prove the particle character in the same measurement, and
conversely
 Einstein’s interpretation: for radiation (photon) intensity
I  (1 / 0 c ) 2  hN   2  N
 2 is a probability measure of photon density
 Max Born: wave function of matter is Y ( x , t ) just as  satisfies wave equation
Y 2 is a measure of the probability of finding a particle in unit volume at a
given place and time. Two superposed matter waves obey a principle of
superposition of radiation.
65
De Broglie’s postulate: wavelike properties of particles
The uncertainty principle
Heisenberg uncertainty principle:
Experiment cannot simultaneously determine the
exact value of momentum and its corresponding
coordinate.
Dp x Dx   / 2
D ED t   / 2
Bohr’s thought experiment:
(1) Dp x  2 p sin  '  ( 2h / l ) sin  '
Dx  l / sin  ' ( a diffraction apparatus a  l /  )
Dp x Dx  ( 2h / l ) sin  '  l / sin  '  2h   / 2
(2) E  p x2 / 2m  DE  2 p x Dp x / 2m  v x Dp x
D x  v x D t  v x  D x / D t  DE  ( D x / D t )D p x
D ED t  D p x D x  2 h   / 2
Bohr’s thought experiment
66
De Broglie’s postulate: wavelike properties of particles
Properties of matter wave
 wave propagation velocity:
h
E
E mv 2 / 2 v
w  l  ( )  ( ) 


p
h
p
mv
2
w  v Why?
 a de Broglie wave of a particle
Y ( x , t )  sin 2p ( x / l  t ) set   1/l
Y ( x , t )  sin 2p (x  t )
(1) x fixed, at any time t the amplitude is one, frequency is ν.
(2) t fixed, Ψ(x,t) is a sine function of x.
n  0,1,2,.......
(3) zeros of the function are at 2p (xn  t )  np
xn  n / 2  t  xn  n / 2  ( /  )t
these nodes move along x axis with a velocity w  dxn / dt   /   l
it is the node propagation velocity (the oscillation velocity)
67
De Broglie’s postulate: wavelike properties of particles
modulate the amplitude of the waves
Y ( x , t )  Y1 ( x , t )  Y2 ( x , t )
Y1 ( x , t )  sin 2p (x  t ),
Y2 ( x , t )  sin 2p [(  d ) x  (  d )t ]
d
d
( 2  d )
( 2  d )
x
t ]  sin 2p [
x
t]
2
2
2
2
d
d
for d  2 and d  2  Y ( x , t )  2 cos[
x
t ]  sin 2p (x  t )
2
2
(1) the velocity of the individual wave is w   / 
 Y ( x , t )  2 cos[
(2) the group velocity of the wave is g 
dν / 2
dν

dκ / 2
d
68
De Broglie’s postulate: wavelike properties of particles
 group velocity of waves equal to moving velocity of particles
E
dE
1
p
dp
 d 
    d 
h
h
l h
h
d dE / h dE
g


d
dp / h
dp
1
dE
E  mv 2
p  mv  dE  mvdv 
v
2
dp
 gv
 
 The Fourier integral can prove the following universal properties
of all wave. DxD  1 / 4p for   1/l , and DtD  1 / 4p
for matter wave : p  h / l  1 / l    p / h
DxD  DxD ( p / h)  (1 / h)DxDp  1 / 4p
 DpDx   / 2
uncertainty principle
E  h    E / h  DtD ( E / h)  (1 / h)DtDE
uncertainty principle
 DEDt   / 2
the consequence
of duality
69
De Broglie’s postulate: wavelike properties of particles
Ex: An atom can radiate at any time after it is excited. It is found that in a
typical case the average excited atom has a life-time of about 10-8 sec. That
is, during this period it emit a photon and is deexcited. (a) What is the
minimum uncertainty D in the frequency of the photon?o (b) Most photons from
sodium atoms are in two spectral lines at about l  5890 A . What is the fractional
width of either line, D /  ? (c) Calculate the uncertainty D E in the energy of the
excited state of the atom. (d) From the previous results determine, to within an
accuracy D E , the energy E of the excited state of a sodium atom, relative to its o
lowest energy state, that emits a photon whose wavelength is centered at 5890 A
(a) DDt  1 / 4p  D  1 / 4pDt  8  10 6 sec-1
(b)   c / l  3  1010 / 5890  10  8  5.1  1014 sec-1
 D/  8  10 6 / 5.1  1014  1.6  10  8 natural width of the spectral line
h / 4p
h
6.63  10  34
8
(c) DE 



3
.
3

10
eV the width of the state
8
Dt
4pDt
4p  10
(d) D/  hD/h   DE / E  E  DE /( D /  )  2.1 eV
70
De Broglie’s postulate: wavelike properties of particles
uncertainty principle in a single-slit diffraction
for a electron beam:
sin  
l
Dy
,
py
p
 sin 
Dp y  p y  p sin  
 Dp y Dy 
pl
Dy
h l

Dy  h 
l Dy
2
71
De Broglie’s postulate: wavelike properties of particles
Ex: Consider a microscopic particle moving freely along the x axis. Assume
that at the instant t=0 the position of the particle is measured and is uncertain
by the amount Dx0 . Calculate the uncertainty in the measured position of the
particle at some later time t.
At t  0  Dp x   / 2Dx0
 Dv x  Dp x / m   / 2m Dx 0
At time t  Dx  tDv x  t / 2m Dx0
Dx0   Dx  or t   Dx 
72
De Broglie’s postulate: wavelike properties of particles

Some consequences of the uncertainty principle:
(1) Wave and particle is made to display either face at will but not both
simultaneously.
 Dirac’s
relativistic
of electron:
E   ofc 2radiation;
p 2  m02c 4
(2) We can
observequantum
either themechanics
wave or the
particle behavior

but assumption:
the uncertainty
principle
prevents
from
observing
Dirac’s
a vacuum
consists
of aus
sea
of electrons
inboth together.
(3) Uncertainty
principle
makes
predictions
onlyatofallprobable
negative
energy levels
which
are normally
filled
points inbehavior
space. of
the particles.
 The philosophy of quantum theory:
(1) Neil Bohr: Copenhagen interpretation of quantum mechanics.
(2) Heisenberg: Principally, we cannot know the present in all details.
(3) Albert Einstein: “God does not play dice with the universe”
The belief in an external world independent of the perceiving subject is
the basis of all natural science.
73
How laser works
Spontaneous emission and stimulated
emission
An excited electron may gives off a photon and decay to
the ground state by two processes:
•spontaneous emission: neon light, light bulb
•stimulated emission : the excited atoms interact with a
pre-existing photon that passes by. If the incoming
photon has the right energy, it induces the electron to
decay and gives off a new photon. Ex. Laser.
Optical pumping
many electrons must be previously excited and held in an
excited state without massive spontaneous emission: this
is called population inversion. The process is called
optical pumping.
Example of Ruby laser.
Optical pumping
Only those perpendicular to the mirrors will be
reflected back to the active medium, They travel
together with incoming photons in the same direction,
this is the directionality of the laser.
Characteristics of laser
• The second photon has the same energy,
i.e. the same wavelength and color as the
first
– laser has a pure color
• It travels in the same direction and exactly
in the same step with the first photon
– laser has temporal coherence
Comparing to the conventional light, a laser is
differentiated by three characteristics. They
are:
Directionality,
pure color,
temporal coherence.
Characteristics of laser
Pure color
Directionality
Temporal coherence
The power and intensity of a
laser
The power P is a measure of energy transfer rate;
Total energy output (J)
Power(W) 
exposurte time (s)
where the unit of power is Joules/s or W.
The energy encountered by a particular spot area
in a unit time is measured by the intensity (or
power density):
Power (W)
Intensity (W/cm ) 
spot area (cm 2 )
2
laser versus ordinary lights:
The directionality of laser beam offers a great advantage
over ordinary lights since it can be concentrate its energy
onto a very small spot area. This is because the laser rays
can be considered as almost parallel and confined to a welldefined circular spot on a distant object.
Sample problem: we compare the intensity of the light
of a bulb of 10 W and that of a laser with output power
of 1mW (10-3 W). For calculation, we consider an
imagery sphere of radius R of 1m for the light
spreading of the bulb, laser beams illuminate a spot of
circular area with a radius
r = 1mm.
Pbulb 10W
10W
5
2
I bulb 



8

10
W
/
cm
A
4pR 2 4p (100cm) 2
Plaser 103W
103W
2
2
I laser 



3

10
W
/
cm
A
pr 2
p (0.1cm)2
I laser 3  102W / cm2

 400
5
2
I bulb 8  10 W / cm
Fluence, F is defined as the total energy delivered
by a laser on an unit area during an expose time TE,
F(J/cm2)=I(watts/cm2) x TE(s)
The advantage of directionality of a laser : we can
focus or defocus a laser beam using a lens. This can
be used to vary the intensity of the laser.
f
Incoming
parallel ray
Focused spot
Diverged
beam
continuous wave (CW) lasers versus
pulsed lasers
• CW lasers has a constant power output during whole
operation time.
• pulsed lasers emits light in strong bursts periodically with
no light between pulses
usually T>>Tw
• The tw may vary from milliseconds (1ms=10-3 s) to
femtoseconds (1fs=10-15s), but typically at
nanoseconds (1ns=10-9s).
• energy is stored up and emitted during a brief time tw,
• this results in a very high instantaneous power Pi
• the average power Pave delivered by a pulsed laser is
low.
Instantaneous power
Average power Pave
Pi
Pi 
E pulse
tw
Pave 
E pulse
T
 E pulse  R
Where R is the repetition rate
Example
A pulsed laser emits 1 milliJoule (mJ) energy that lasts for
1 nanoseconds (ns), if the repetition rate R is 5 Hz,
comparing their instantaneous power and average power.
(The repetition rate is the number of pulses per second, so
the repetition rate is related to the time interval by R=1/T).
Pi 
E pulse
Pave 
tw
1mlliJoule 103 J

 9  106W
1ns
10 s
E pulse
T
 E pulse( J )  R( Hz )  103 J  5Hz  5  103W
Mechanisms of laser
interaction with human tissues
When a laser beam projected to
tissue
Five phenomena:
•reflection,
•transmission,
•scattering,
•re-emission,
•absorption.
Laser light interacts
with tissue and transfers
energy of photons to
tissue
because absorption
Photocoagulation
What is a coagulation?
• A slow heating of muscle and other tissues is like a
cooking of meat in everyday life.
• The heating induced the destabilization of the
proteins, enzymes.
• This is also called coagulation.
• Like egg whites coagulate when cooked, red meat
turns gray because coagulation during cooking.
ALsrhtigotissusbov50oCbutblow
100oC iducsdisordrigoprotisdothr
bioolculs,thisprocssisclld
photocogultio.
Consequence of photocoagulation
When lasers are used to photocoagulate tissues during
surgery, tissues essentially becomes cooked:
• they shrink in mass because water is expelled,
• the heated region change color and loses its
mechanical integrity
• cells in the photocoagulated region die and a region
of dead tissue called photocoagulation burn
develops
• can be removed or pull out,
Applications of photocoagulation
• destroy tumors
• treating various eye conditions like retinal
disorders caused by diabetes
• hemostatic laser surgery - bloodless incision,
excision:
due to its ability to stop bleeding during
surgery. A blood vessel subjected to
photocoagulation develops a pinched point due
to shrinkage of proteins in the vessel’s wall.
The coagulation restriction helps seal off the
flow, while damaged cells initiate clotting.
Photo-vaporization
With very high power densities, instead of cooking,
lasers will quickly heat the tissues to above 100o C ,
water within the tissues boils and evaporates. Since 70%
of the body tissue is water, the boiling change the tissue
into a gas. This phenomenon is called photovaporization.
Photo- vaporization results in complete removal of the
tissue, making possible for :
• hemostatic
incision,or
excision.
• complete removal
of thin layer of
tissue. Skin
rejuvenation,
Conditions for photo-vaporization
1. the tissue must be heated quickly to above the
boiling point of the water, this require very high
intensity lasers,
2. a very short exposure time TE, so no time for heat
to flow away while delivering enough energy,
highly spatial coherence
(directionality) of lasers
over other light sources
is responsible for
providing higher
intensities
Intensity requirement
Intensity (W/cm2)
Low (<10)
Moderate (10 – 100)
High (>100)
Resulting processes
General heating
Photocoagulation
Photo-vaporization
Photochemical ablation
When using high power lasers of ultraviolet
wavelength, some chemical bonds can be broken
without causing local heating; this process is called
photo-chemical ablation.
The photo-chemical ablation results in clean-cut
incision. The thermal component is relatively small and
the zone of thermal interaction is limited in the incision
wall.
Selective absorption of
laser light by human tissues
Selective absorption
Selective absorption occurs when a given color of light
is strongly absorbed by one type of tissue, while
transmitted by another. Lasers’ pure color is responsible
for selective absorption.
The main absorbing components of tissues are:
• Oxyhemoglobin (in blood): the blood’s oxygen
carrying protein, absorption of UV and blue and
green light,
• Melanin (a pigment in skin, hair, moles, etc):
absorption in visible and near IR light (400nm –
1000nm),
• Water (in tissues): transparent to visible light but
Selective absorption
Applications of lasers