QUANTUM
MECHANICS
Light as a
Particle
- Describe the photon model of light and explain how the
wavelength/frequecy and amplitude/intensity of a light beam are related
to the underlying properties of the photons
Properties of
Quanta of Light ("Photons")
- predict the likelihood of various outcomes in simple experiments governed by probabilistic behavior
- to relate the macroscopic properties of a light beam (wavelength, power) to properties of photons
The quantum description of particles
- describe the double slit experiment for light or electrons
and explain why this provides evidence that quantum particles do not
have definite positions and can exist in quantum superpositions
- explain why the results of the double slit experiment imply
that the initial electrons do not have
well defined positions
- explain
why the double slit experiment suggests that the behavior of
single particles is probabalistic and how the classical intensity
pattern is related to the relative probability for hitting various
points on the screen
- Describe what is meant by
probability density and evaluate whether or not a given function is a
valid probability density for finding a particle
- Explain what is meant by a position eigenstate and describe what the wavefunction looks like for such a state.
- Use
the wavefunction to determine the probability for finding a particle in
a given region of space.
- Explain what happens to the wavefunction after a measurement of the particle's position
Momentum eigenstates, wavepackets, and uncertainty- explain why the double slit experiment suggets that we can associate a wavelength to electrons with a particular momentum
- state de Broglie’s relationship between wavelength and
momentum of an electron or other particle
- describe the wavefunction for a particle with definite momentum
- explain
what is meant by a wavepacket and why the wavefunction for a real
travelling electron should take this form instead of a pure wave
- give a simple explanation for why particles with well defined momentum cannot have a definite position
- explain
the physical interpretation of the mathematical fact that wavepackets
and other wavefunctions can be written as a sum of pure waves
- explain
qualitatively how the width of a wavepacket and its wavelength relate
to the combination of pure waves (momentum eigenstates) that it is
built from
- describe how properties of a wavepacket (wavelength, width) will affect the subsequent evolution of the wavepacket.
- explain what is meant by uncertainty in position and uncertainty in momentum for a state.
The
Schrödinger
Equation
- predict the velocity of a given wavepacket by looking at the wavepacket at some initial time
- to
qualitatively describe the time evolution of a wavefunction that is a
pure wave, and describe how this evolution depends on the wavelength.
- given two wavepackets, predict which will spread out faster
- explain
why the speed of electron wavepackets should be inversely
proportional to wavelength
- to
predict the frequency of oscillation of an electon's wavefunction,
given the wavelength and the potential energy in the region
- explain
why knowing the time dependence of momentum eigenstate wavefunctions
allows us to determine the time-dependence for general wavefunctions
(of a free particle)
- explain why the Schrodinger equation determines the time-dependence of a wavefunction
- write
down the potential function for simple physical
systems including electrons in wires or electrons near other charges
Bound states and
atomic spectra
- Explain how to tell, by watching a movie of a wavfunction
evolving with time, whether the particle being described is in a state
of definine energy
- explain
the crucial difference between the allowed energies for bound states in
quantum mechanics as compared to classical mechanics