1 Course Summary
1.1 Problems with Classical Physics
Around the beginning of the 20th century,classical physics,based on Newtonian Mechanics and
Maxwell’s equations of Electricity and Magnetism described nature aswe knew it. Statistical Me-
chanics was also a well developed discipline describing systems with a large number of degrees of
freedom. Around that time, Einstein introduced Special Relativity which was compatible with
Maxwell’s equations but changed our understanding of space-time and modified Mechanics.
Many things remained unexplained. While the electron as a constituent of atoms had been found,
atomic structure was rich and quite mysterious. There were problems with classical physics, (See
section 2) including Black Body Radiation, the Photoelectric effect, basic Atomic Theory, Compton
Scattering, and eventually with the diffraction of all kinds of particles. Plank hypothesized that EM
energy was always emitted in quanta
E=hν= ̄hωto solve the Black Body problem. Much later, deBroglie derived the wavelength (See section 3.4)
for particles.
λ=h
pUltimately, the problems led to the development of Quantum Mechanics in which all particles are
understood to have both wave and a particle behavior.
1.2 Thought Experiments on Diffraction
Diffraction (See section 3) of photons, electrons, and neutrons has been observed (see the pictures)
and used to study crystal structure.
To understand the experimental input in a simplified way, we considersome thought experiments on
the diffraction (See section 3.5) of photons, electrons, and bulletsthrough two slits. For example,
photons, which make up all electromagnetic waves, show a diffraction pattern exactly as predicted
by the theory of EM waves, but we always detect an integer numberof photons with thePlank’s
relation,E=hν, between wave frequency and particle energy satisfied.
Electrons, neutrons, and everything else behave in exactly the same way, exhibiting wave-like diffrac-
tion yet detection of an integer number of particles and satisfyingλ=hp. This deBroglie wavelength
formula relates the wave propertyλto the particle propertyp.
1.3 Probability Amplitudes
In Quantum Mechanics, we understand thiswave-particle dualityusing (complex) probability
amplitudes (See section 4) which satisfy a wave equation.
ψ(~x,t) =ei(
~k·~x−ωt)
=ei(~p·~x−Et)/ ̄h