Introduction to Quantum Mechanics II
Physics 3373 Syllabus
Three Static Approximation Methods
Time-independent perturbation theory
Examples of time-independent perturbation theory
Aspects of degenerate perturbation theory
WKB semiclassical approximation
Use of WKB approximation in barrier penetration
Use of WKB approximation in bound states
Variational methods
The Three-Dimensional Radial Equation
Recap of the situation
The free particle
The infinite spherical well potential
The “deuteron” (finite potential well)
The Coulomb potential-initial considerations
The Coulomb potential-2D harmonic oscillator comparison
The “Confined Coulombic Model”
Addition of Angular Momenta
General angular momentum eigenstate properties
Combining angular momenta for two systems
Explicit example of adding two spin 1/2 systems
Explicit example of adding orbital angular momentum and spin 1/2
Hydrogen atoms and the choice of basis states
Hydrogen atom and perturbative energy shifts
Time-Dependent Systems
Time-dependent potentials
Sudden and slow quantum transitions
Two-state problems
The Berry phase
Magnetic spin resonance and the geometrical phase
The Aharonov-Bohm effect
Time-dependent perturbation theory and transitions
Applications of Fermi’s Golden Rule
Exponential time decay and decay widths
Quantum Particle Scattering
The one-dimensional integral Schrodinger equation
Reflection and transition amplitudes
One-dimensional delta-function scattering
Step-function potential scatterimng
The Born series
The three-dimensional integral Schrodinger equation
The Helmholtz equation and plane waves
Cross sections and the scattering amplitude
Scattering phase shifts
Finite-trange potential scattering
The three-dimensional Born series
Identical particle scattering
Proton-proton scattering
Connecting to the Standard Model
Discrete Symmetries
Parity
Time Reversal
Charge Conjugation
Particle primer
Particle interactions
Quantum electrodynamics
Quantum chromodynamics
Weak Interactions
Supersymmetry
Superstrings
Postlude
Appendix G: Quantum Computing