Transcript Recherches sur la théorie des quanta

Introduction to Quantum
Physics
Early Atomic Physics
What is Quantum Physics
Quantum Physics is a collection of laws
which explain observations of the tiny
building blocks of all matter.
The world of the quantum must be able to
explain the classical world that we live in.
To understand the quantum world we
need to understand one of the major
building blocks ---- the atom
History of Atomic Structure
The model of atomic structure has
changed as observations have altered our
perceptions
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Democrictus
Dalton
Thomson
Rutherford
………. (The model is not complete)
Democritus
Atoms (Greek for indivisible) are the
smallest unit of matter
Atoms share all of the properties of the
macroscopic object
Atoms are the smallest pieces of matter
which still act as the material from which
they come from
John Dalton
First truly scientific theory of the atom
(results discovered through experiments
with marsh gases)
Proof of early Greek model --- the atom is
indivisible but with no internal
structure
Properties of matter come
from the properties of the atom
But what about electricity?
J.J. Thomson
Discoverer of the electron
The atom consists of a positively charged
substance (like pudding) containing
negative charges (like the raisins in a plum
pudding)
Rutherford
1909 – Rutherford performs an experiment
in which alpha particles (He nucleus) are
fired towards a thin foil of gold
Rutherford
Experimental observations indicated that
the majority of the alpha particles passed
straight through, with few being deflected
at small angles and even fewer retro
reflecting from the gold foil
Rutherford
Observations indicate that the atom is
mostly empty space with a dense, central,
positively-charged structure at its center
The electrons (discovered by Thomson)
must therefore exist outside of this central
nucleus …. Orbiting around the nucleus as
planets do the Sun.
Classical Model
The Rutherford model of the atom became
known as the classical model of the atom
Problem with the classical Model
The Theory
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The electron has a negative charge and orbits about
the central nucleus
The central nucleus has a charge and therefore must
also have a magnetic field
Charged particles lose energy as they pass through a
magnetic field
According to classical electro-magnetic
theory the electron should lose energy in
its orbit.
Observations
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The atom is a stable structure consisting of
sub atomic particles that do not normally
decay in our life time.
Because the observation does not match
the theory …. either classical physics is
wrong OR the Rutherford model is wrong /
incomplete
Which is easier to believe ?
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Hundreds of years of Physics laws and
theories are wrong.
A relatively new model of our atom is wrong.
Answer :
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Both classical physics and the Rutherford
model have some minor problems.
But it is our picture of the atom which is mostly
incorrect.
Enter Niels Bohr
Bohr succeeded in solving the problem
with the classical model by uniting two
disparate ideas : Planck’s quanta and the
hydrogen emission spectra
Max Planck
Observed the temperatures of cannons as
they were bored out
The colour of the emitted
radiation is related to the
temperature of the cannon
The expected peak intensity
follow the Rayleigh-Jean
law
Rayleigh-Jean Law
Ultraviolet Catastrophe
The classical (Rayleigh-Jeans) model
predicted a steady increase in Intensity
well into the ultraviolet
If the theory worked with
the cannons then enough
ultraviolet radiation would
be emitted to destroy life.
Energy is not continuous
Planck solved the “catastrophe” by reimagining Energy
Energy is not a continuous stream but
consists of chunks or discrete packets
Energy is quantized (flows as quanta)
Planck did not initially believe in his
findings
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Why would energy be quantized … it is
neither simple or beautiful
Planck’s findings were instrumental in the
work for which Einstein won the Noble
Prize in Physics
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Photoelectric Effect
Quanta of Energy
Vibrating molecules can only vibrate with
certain discrete amounts of energy
Each quanta of energy can be determined
by E = hf
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E is the energy of the Quanta (J or eV)
f is the frequency of the vibration
h is Planck’s constant (6.626 x 10-34 Js)
Hydrogen emission spectra
Bohr also received a clue from the
emission spectra of the Hydrogen atom
Again the classical model predicts that the
atom should be able to radiate in an
infinite range of wavelengths but
observations indicate otherwise
Energy is quantized
If the electron in the atom can only absorb
or emit discrete quantities of energy
(quanta) then the emission spectra makes
sense
By using Planck’s hypothesis and the
clues from the emission spectra of
Hydrogen Bohr was able to
mathematically explain the nature of the
atom
Hydrogen emission spectra
Bohr’s theory
Bohr’s theory was the first step in the Quantum
revolution
Postulate of Stationary States : the Hydrogen
atom can exist, without radiating energy, in any
one of a discrete set of orbits of fixed energy
Frequency Postulate : the Hydrogen atom can
emit or absorb a quantity of energy only when
the electron changes from one stationary state
into another. This amount can be calculated by
E=hf
Question
How does the concept of the quantization
of energy circumvent the problem with the
classical model?
The Atom so far ….
A central nucleus (of positive charge) is
surrounded by negatively charged
particles called electrons
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Electrons can only orbit in fixed distances
from the nucleus because they can only gain /
lose a quanta of energy
This prevents the electron from “falling into” the
nucleus
Problems with the Bohr model
1. The two postulates only work with the
Hydrogen atom. When the model is
applied to other atoms … extra
dimensions of space is required.
2. The works of Grimaldi have shown that
electrons are capable of displaying an
interference pattern. How could a particle
do this?
• Both of these problems can be “solved” to
create a new theory by applying the
works of deBroglie and Schrodinger.
Louis de Broglie
• First degree in History but applied for
graduate work in Physics
• Doctoral thesis Recherches sur la théorie
des quanta
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Work beyond the intellect of his professors
Sent to Einstein who endorsed it fully
Matter Waves
De Broglie proposed that all matter have
both matter properties and wave
properties.
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Start with the Einstein energy-matter equality
E = mc2
This energy is quantized according to Planck
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So E = hf = mc2
hf = mc2
hf = (mc)c
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mc is the momentum of the wave = p
hf = pc
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v = fl
hf = p(fl)
h = pl
So p = h / l
In short … any piece of matter travelling at
any speed can exhibit wave properties
The effects for classical particles are too
small to observe
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The electron is not only a particle but also
displays wave nature
Therefore the electron can diffract
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Light also displays both particle and wave
nature
Bohr model – revision #1
The atom consists of
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A massive positively charged central nucleus
Negatively charged electrons which create
standing waves of energy.
These waves of energy can only vibrate / resonate
at specific frequencies
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These frequencies determine the orbitals around the
nucleus
de Broglie matter waves do not solve the
multi-dimensionality problem!
Enter Schrodinger
Einstein given the task to apply the
Bohr/de Broglie model to atoms other than
Hydrogen
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Was too busy working on GUT so he passed
the task on to his friend Erwin Schrodinger
Schrodinger was an unpopular choice in that
he was considered a failed Physicist!
Christmas holidays and New Years 192526
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Schrodinger takes his mistress into the Alps
on vacation
It is here that he comes up with his wave
equation for all matter
This set of equations works for all atoms --- not just
Hydrogen
The Schrodinger wave model
de Broglie’s matter waves do not describe
the physical location of the electrons
around the nucleus
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The mathematics describes the probability of
finding the electron in a given location of
space
Loss of determinism?!?!?
All life is based on probability … there are no
definite knowns!
“God does not play dice with the Universe”
Implications of a Probabilistic
Universe
Quantum tunneling
HUP
Schrödinger's cat
BEC
Separation of classical world and quantum
world
Quantum Tunneling
Imagine that you have a single electron
that you place into an electrical potential
well. The electron requires an infinite
amount of energy to climb out of the box.
Where is the electron?
Now imagine that you leave the electron
and return to it a few weeks later.
Where is the electron now?
Classical Physics would tell us that the
electron must always be in the
electropotential well … since it doesn’t
have enough energy to “climb out”
Experimental evidence indicates that the
electron will leak out over time!!!
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This is the process through which
semiconductors work
The Schrodinger equation defining the
position of the electron is both energy, and
time dependent
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As time proceeds the probability of finding the
electron in a set location begins to smear out
over space.
There is a probability that the electron can
“climb out” of the electropotential well.
Heisenberg’s Uncertainty
Principle
Two versions of HUP
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Uncertainty between knowing the momentum
of an object and the exact position of an
object
Uncertainty between knowing the amount of
energy a substance contains within a time
interval of measurment
Momentum and position
Imagine that we have a small sub atomic
particle that we want to observe and
record all possible data for.
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We start to attempt to measure the
momentum of the object
To measure the velocity (and therefore the
momentum) we need to set up a set of timing
gates
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We can use low energy x-rays to record the
passage of the sub atomic particle from one
gate to the other
This will allow us to measure the velocity and
therefore the momentum
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The wavelength of the x-ray is too long at low
energies so even though we can use it to
measure the momentum we can not use it to
determine the exact position.
We can increase the energy of the x-ray
which results in a tighter wavelength
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This will allow us to know the exact location of
our subatomic particle
But the increase in energy imparts energy to our
sub atomic particle changing it’s motion direction
…. And therefore changing the momentum
So
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By measuring the momentum the exact
position remains unknown
By measuring the exact position we change
the momentum
We can not know the exact position and
momentum at the same time.
A similar uncertainty exists between
energy and time
Schrodinger’s Cat
The macroscopic / classical physicists
rebuttal to HUP
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Classical physicists refuse to believe that
It is impossible to know everything about a system
The act of observing a system changes the system
... The act of experimentation destroys
determinism