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6.1.1.
Foundations of Quantum Mechanics
– Particles & Waves <CJ chap 29 >
6.1.1.1.
Discussion
6.1.1.1.1.
Cavity
radiation refers to EM radiation from a hole inside a substance -also called
blackbody radiation
6.1.1.1.1.1.
Is dependent upon the temperature
and independent of the substance making the cavity
6.1.1.1.1.2.
Cavity radiation was found to have a
wavelength spectra that could not be explained by theory
6.1.1.1.1.3.
Plank (1900) proposed that the walls
consist of oscillators that emit & absorb only certain quanta
6.1.1.1.1.4.
where Eem = n h f where n = 1,2,.. f = the frequency of radiation, and h
is a constant 6.626E-34
6.1.1.1.2.
Photoelectric
effect is the emission of electrons from a metal when radiated by ultraviolet
light
6.1.1.1.2.1.
Problem 1: The energy of the
electrons is independent of the light intensity but depends only on f
6.1.1.1.2.2.
Problem 2: Below a given f of light,
no electrons are emitted no matter how intense the light is
6.1.1.1.2.3.
Problem 3: The effect of emission is
immediate no matter how low the intensity
6.1.1.1.2.4.
These problems were counter to the
Maxwell theory of EM radiation as was cavity radiation
6.1.1.1.3.
Einstein
explained both phenomenon and founded quantum theory postulating photons that Eem =hf
6.1.1.1.3.1.
Thus light consisted of these
‘quanta’ of pure massless energy also with momenta P=h/l
6.1.1.1.3.2.
Thus the view of EM radiation as
oscillating E and B fields is only an approximation to photons
6.1.1.1.4.
Arthur
Compton in 1923 scattered photons from electrons and showed that l’-l =
(h/mc)(1-cosq)
6.1.1.1.4.1.
This confirmed the Einstein photon
hypothesis experimentally
6.1.1.1.5.
Louis
De Broglie in 1923 proposed that the same photon equations Eem =hf, p=h/l apply to matter
6.1.1.1.5.1.
Thus given a particles energy E and
momentum p, one can compute an associated f & l
6.1.1.1.5.2.
In 1927, Davisson & Germer &
Thompson confirmed wave interference effects scattering e-
6.1.1.1.5.3.
This scattering of e- from a crystal gave interference patterns only possible for a wave like X rays
6.1.1.1.6.
In
1925, Erwin Schrödinger proposed his equation for the ‘motion’ of this ‘matter
wave’ Y(x,y,z,t)
6.1.1.1.7.
In
1925 Werner Heisenberg also proposed an alternate formulation for Y in terms of matrix theory
6.1.1.1.8.
In
1926 P.A.M. Dirac presented a unifying mathematical theory that showed these
theories equivalent
6.1.1.1.9.
Heisenberg
later showed that Y contains information on both the
particles position and momenta BUT
6.1.1.1.9.1.
to know more about the position one
looses knowledge of the momenta and conversely as:
6.1.1.1.9.2.
Heisenberg uncertainty principle
gives the product of these uncertainties as Dx Dp >= h/4p
6.1.1.1.9.3.
Also one has an equivalent equation
for energy and time: Dt DE >= h/4p
6.1.1.1.9.4.
Heisenberg’s uncertainty principle
has deep implications for what is simultaneously knowable
6.1.1.2.
Mathematical
6.1.1.3.
Advanced