Transcript wave function

The Nature of Light
Is Light a Particle or a Wave?
The Particle Theory of Light
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Light is considered to be a stream of particles
Isaac Newton was the chief architect of the particle
theory of light.
Phenomena of light can be explained by the particle
theory
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Reflection, Refraction
Two phenomena of light can not be explained by the
particle theory
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Interference: The first demonstration by Thomas Young in 1801
Diffraction
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The Wave Theory of Light
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In 1678, Dutch physicist, Christian Huygens,
showed a wave model of light that can explains also
the reflection and refraction of light.
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Diffraction
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Interference: Young’s double-slit
experiment
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History of Wave Theory
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In 1801, Thomas Young provided the first clear
demonstration of the wave nature of light
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In 1865, Maxwell asserted that light was a form of highfrequency electromagnetic wave and no medium is
required for the propagation of light
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In 1887, Hertz confirmed Maxwell’s predictions
During the 19-th century, other developments led to the
general acceptance of the wave theory of light
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New Phenomena support the
Particle Theory of Light
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Blackbody radiation
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The photoelectric effect
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The Compton scattering
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Dual nature of light
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Now, we accept that light has a dual
nature.
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In some cases, light behaves like a
wave, and in others, light behaves like a
particle.
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Blackbody Radiation: Thermal
radiation of a blackbody at T
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Planck’s Theory of
Blackbody Radiation
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In 1900, Planck assumed the
cavity radiation came from
atomic oscillations in the cavity
walls
Assumption (I): The energy of
an oscillator can have only
certain discrete values En
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En = n h ƒ
Assumption (II): The oscillators
emit or absorb energy only in
discrete units
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The photoelectric effect
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First discovered by Hertz
The photoelectric effect occurs
when light incident on certain
metallic surfaces causes electrons
to be emitted from those surfaces
Einstein extended Planck’s concept
of quantization to electromagnetic
waves
All electromagnetic radiation can be
considered a stream of quanta, now
called photons
A photon of incident light gives all its
energy hƒ to a single electron in the
metal
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The Compton Effect
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The scattering of X-ray from free electron
The results could be explained by treating
the photons as point-like particles having
energy hƒ and momentum hƒ / c
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Dual Nature of Light: Photons
and Waves
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Some experiments are best explained by the
photon model
Some are best explained by the wave model
The nature of light is not describable in terms
of any single classical model
Light has a dual nature in that it exhibits both
wave and particle characteristics
The particle model and the wave model of
light are complement each other
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Wave Properties of Particles
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In 1923, de Broglie postulated that all matters
have both wave and particle properties
The de Broglie wavelength of a particle is

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h
h

p mv
The particles would also have a frequency
E
ƒ
h
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Davisson-Germer Experiment
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If particles have a wave nature,
they should exhibit diffraction
effects
In 1927, Davission and Germer
measured the wavelength of
electrons by the diffraction of
electrons from single crystals
This provided experimental
confirmation of the matter
waves proposed by de Broglie
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Quantum Particle
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The quantum particle is a model for the dual nature
of light and of material particles
In this model, entities have both particle and wave
characteristics
We much choose one appropriate behavior in order to
understand a particular phenomenon
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The Uncertainty Principle
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In classical mechanics, it is possible to
make measurements with arbitrarily
small uncertainty
Quantum theory predicts that it is
fundamentally impossible to make
simultaneous measurements of a
particle’s position and momentum with
infinite accuracy
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Heisenberg Uncertainty Principle
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The Heisenberg Uncertainty Principle
states if a measurement of the position
of a particle is made with uncertainty Dx
and a simultaneous measurement of its
x component of momentum is made
with uncertainty Dp, the product of the
two uncertainties can never be smaller
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than
DxDp 
x
2
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Heisenberg Uncertainty Principle,
Another Form
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Another form of the Uncertainty
Principle can be expressed in terms of
energy and time
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DEDt 
2
This suggests that energy conservation
can appear to be violated by an amount
DE as long as it is only for a short time
interval Dt
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Wave Function –
Probability Interpretation
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The amplitude of the wave associated with the
particle is called the probability amplitude or
the wave function Y
The wave function is often complex-valued
|y|2 = y*y is always real and positive
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y* is the complete conjugate of y
It is proportional to the probability per unit volume of
finding a particle at a given point at some instant
The wave function contains within it all the
information that can be known about the
particle
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Schrödinger Equation for Wave
function
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Erwin Schrödinger proposed a wave equation
that describes the manner in which the wave
function changes in space and time
The Schrödinger equation for a particle of
mass m confined in a potential energy function
U(x) is
h 2 d 2y

 Uy  Ey
2
2m dx
This is called the time-independent
Schrödinger equation
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Quantum Tunneling
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Classically, the particle is
reflected by the barrier
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Regions II and III would be
forbidden
According to quantum
mechanics, all regions are
accessible to the particle
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The probability of the particle
being in a classically forbidden
region is low, but not zero
Application: Scanning tunneling
microscope
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Early Models of the Atom –
Newton’s Time
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The atom was a tiny, hard indestructible
sphere
It was a particle model that ignored any
internal structure
The model was a good basis for the
kinetic theory of gases
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Early Models of the Atom –
JJ Thomson
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J. J. Thomson
established the charge
to mass ratio for
electrons
His model of the atom
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A volume of positive
charge
Electrons embedded
throughout the volume
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Rutherford’s
Thin Foil Experiment
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In 1911, Rutherford
performed an experiment to
show that Tomson’s model
was not correct
A beam of positively
charged alpha particles hit
and are scattered from a
thin foil target
Large deflections could not
be explained by Thomson’s
model
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Early Models of the Atom –
Rutherford
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Rutherford
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Planetary model
Based on results of thin
foil experiments
Positive charge is
concentrated in the center
of the atom, called the
nucleus
Electrons orbit the
nucleus like planets orbit
the sun
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Difficulties with the
Rutherford Model
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Rutherford’s electrons are
undergoing a centripetal
acceleration
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The electrons should radiate EM
waves of the same frequency
The radius should steadily decrease as
this radiation is given off
The electron should eventually spiral
into the nucleus
Rutherford model is unable to
explain certain discrete
characteristic frequencies of EM
radiation emitted by atoms
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29.1 Importance of the
Hydrogen Atom
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The hydrogen atom is the only atomic
system that can be solved exactly
Much of what was learned about the
hydrogen atom, with its single electron,
can be extended to such single-electron
ions as He+ and Li2+
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More Reasons the
Hydrogen Atom is Important
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The hydrogen atom proved to be an ideal
system for performing precision tests of
theory against experiment
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Also for improving our understanding of atomic
structure
The quantum numbers that are used to
characterize the allowed states of hydrogen
can also be used to investigate more complex
atoms
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This allows us to understand the periodic table
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Final Reason for the Importance
of the Hydrogen Atom
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The basic ideas about atomic structure
must be well understood before we
attempt to deal with the complexities of
molecular structures and the electronic
structure of solids
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