Transcript Birth_QM

Birth of Quantum Mechanics
PHYS 311
Necessity of QM
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By the end of the nineteenth century a number of serious
discrepancies had been found between experimental results and
classical theory.
 Blackbody radiation law
 Photo-electric effect
 Atom and atomic spectra
Blackbody radiation
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Exp. Measurements: the
radiation spectrum was well
determined --- a continuous
spectrum with a shape that
dependent only on temperature
Blackbody radiation
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Exp. Measurements: the
radiation spectrum was well
determined --- a continuous
spectrum with a shape that
dependent only on temperature
Theory: classical kinetic theory
(Rayleigh and Jeans) predicts
the energy radiated to increase
as the square of the frequency.
Completely wrong! Ultraviolet
catastrophe!
Planck’s solution
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Planck’s assumption (1900): radiation of a given frequency ν
could only be emitted and absorbed in “quanta” of energy E=hν
h=6.6261E-34 J·s : Planck’s constant
With this assumption, Planck came up with a formula that fits
well with the data.
Planck called his theory “an act of desperation”.
Planck’s solution
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Planck’s assumption (1900): radiation of a given frequency ν
could only be emitted and absorbed in “quanta” of energy E=hν
h=6.6261E-34 J·s : Planck’s constant
With this assumption, Planck came up with a formula that fits
well with the data.
Planck called his theory “an act of desperation”.
Planck neither envisaged a quantization of the radiation field,
nor did he quantize the energy of an individual material
oscillator
What Planck assumed is that the total energy of a large number
oscillators is made up of finite energy elements hν
Einstein’s interpretation of Planck’s formula
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Einstein in 1906 interpreted Planck’s result as follows:
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“Hence, we must view the following proposition as the basis
underlying Planck’s theory of radiation: The energy of an
elementary resonator can only assume values that are
integral multiples of hν; by emission and absorption, the energy
of a resonator changes by jumps of integral multiples of hν”
Photo-electric effect
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Experimental facts
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Shining light on metal can liberate electrons from metal
surface
Whether the metal emit electrons depends on the freq. of
the light: only light with a freq. greater than a given
threshold will produce electrons
Increasing the intensity of light increases the number of
electrons, but not the energy of each electron
Energy of electron increases with the increase of light
frequency.
Einstein on photo-electric effects
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Light consists of a collection of “light quanta” of energy hν
The absorption of a single light quantum by an electron
increases the electron energy by hν
Some of this energy must be expended to separate the electron
from the metal (the work function, W), which explains the
threshold behavior, and the rest goes to the kinetic energy of
the electron.
Electron kinetic energy = hν - W
Reactions to Einstein’s light quanta idea
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For a long, long time, nobody else believed that.
Reactions to Einstein’s light quanta idea
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For a long, long time, nobody else believed that.
Planck and others in their recommendation of Einstein’s
membership in Prussian Academy (1913):
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“One can say that there is hardly one among the great problems in
which modern physics is so rich to which Einstein has not made a
remarkable contribution. That he may sometimes have missed the
target in his speculations, as, for example, in his hypothesis of light
quanta, cannot really be held to much against him, for it is not
possible to introduce really new ideas even in the most exact
sciences without sometimes taking a risk
Experimental confirmation
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Experimental confirmation came in 1915 by Millikan
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Millikan didn’t like Einstein’s light quanta idea, which he saw as an
attack on the wave theory of light.
Tried very hard (for 10 years) to disprove Einstein’s theoretical
prediction.
Experimental confirmation
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Experimental confirmation came in 1915 by Millikan
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Millikan didn’t like Einstein’s light quanta idea, which he saw as an
attack on the wave theory of light.
Tried very hard (for 10 years) to disprove Einstein’s theoretical
prediction.
For all his efforts, he confirmed Einstein’s theory and provided a
very accurate measurement of Planck’s constant.
Millikan got Nobel prize in 1923.
Experimental confirmation
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Experimental confirmation came in 1915 by Millikan
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Millikan didn’t like Einstein’s light quanta idea, which he saw as an
attack on the wave theory of light.
Tried very hard (for 10 years) to disprove Einstein’s theoretical
prediction.
For all his efforts, he confirmed Einstein’s theory and provided a
very accurate measurement of Planck’s constant.
Millikan got Nobel prize in 1923.
Still didn’t like Einstein’s light quanta idea, in a 1916 paper:
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“This hypothesis may well be called reckless …”
“Despite the apparently complete success of the Einstein equation, the
physical theory of which it was designed to be the symbolic expression
is found so untenable …”
Einstein on light quanta
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“All these fifty years of conscious brooding have
brought me no nearer to the answer to the question
`What are light quanta?’ Nowadays every rascal
thinks he knows, but he is mistaken.”
--- letter to Michel Besso, 1951
Problems with atomic stability
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Rutherford’s experiment (1911): atom is composed of
electrons moving around a heavy nucleus.
Problems with atom stability
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Rutherford’s experiment (1911): atom is composed of
electrons moving around a heavy nucleus.
Problem: if the electrons orbit the nucleus, classical
physics predicts they should emit electromagnetic
waves and loose energy.
If this happens, the electron will spiral into the
nucleus, no stable atom should exist!
Problems with atomic spectrum
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Atomic radiation spectrum consists of discrete lines.
Bohr’s solution (1912)
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An atomic system can only exist
in a discrete set of stationary
states, with discrete values of
energy.
Change of the energy, including
emission and absorption of
light, must take place by a
complete transition between
two such stationary states.
Bohr’s solution (1912)
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An atomic system can only exist in a discrete set of stationary
states, with discrete values of energy.
Change of the energy, including emission and absorption of
light, must take place by a complete transition between two
such stationary states.
The radiation absorbed or emitted during a transition between
two states of energies E1 and E2 has a frequency: hν=E1 - E2
Bohr’s formula explains some of the spectral lines in hydrogen
atom (but not all), does not do well with other atoms.
Bohr’s solution (1912)
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An atomic system can only exist in a discrete set of stationary
states, with discrete values of energy.
Change of the energy, including emission and absorption of
light, must take place by a complete transition between two
such stationary states.
The radiation absorbed or emitted during a transition between
two states of energies E1 and E2 has a frequency: hν=E1 - E2
Bohr’s formula explains some of the spectral lines in hydrogen
atom (but not all), does not do well with other atoms.
A truly revolutionary idea, even Einstein was impressed:
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“… appeared to me like a miracle. This is highest form of musicality
in the sphere of thought.” (1951)
summary
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Energy quantization is necessary to explain the
blackbody radiation, the photo-electric effects, the
stability of atoms and their spectra
Classical physics must be given up: physical
properties that are quantized and not continuous are
completely different from the ideas of continuous
space and time in classical physics.
Later developments
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De Broglie: matter wave λ=h/p
Exp. with electron diffraction (Davisson and Germer, 1927)
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Today: interferometers with neutrons, atoms and molecules
Born’s statistical interpretation of matter wave
Matrix mechanics (Heisenberg, Born and Jordan)
Wave mechanics, Schroedinger’s equation (Schroedinger)
Relativistic QM (Dirac)
Exclusion principle (Pauli)
Birth of QM
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The necessity for quantum mechanics was thrust upon us by a
series of observations.
The theory of QM developed over a period of 30 years,
culminating in 1925-27 with a set of postulates.
QM cannot be deduced from pure mathematical or logical
reasoning.
QM is not intuitive, because we don’t live in the world of
electrons and atoms.
QM is based on observation. Like all science, it is subject to
change if inconsistencies with further observation are revealed.
Goal of PHYS311 and 312
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We will study non-relativistic QM.
Our goal is to understand the meaning of the postulates the
theory is based on, and how to operationally use the theory to
calculate properties of systems.
The first semester will lay out the ground work and
mathematical structure, while the second will deal more with
computation of real problems.