Fall 2018 Syllabus PhysicsV2500

Syllabus for Phys. V2500 (Phys. 725): Quantum Mechanics I Text (Fa112018): QM, by Franz Schnabl, (4th edition)

Topics Covered:

Historical Survey

Specific heat

Black-body Radiation Photo-electric effect

Photons, Einstein A-B coeff. Compton effect

Rutl'\erford atom Bohr model

Bohr-Sommerfeld rules DeBroclie Waves

Fourier Series and Inteirals 3-functions

informal uncertainty prin.

3-D wave packets

phase and group velocity Schroedincer Eq . for free particles

.,Copenhagen Interpretation

Formal uncertainty relation Complementarity

coherence and superposition discussion of examples of u.p. 11hidden variables11

Operators in OM- prelim. treatment Schroedineer eg. with forces

momentum space

time-dependence  of solns. Ehrenfest Theorem

Time-Independent  problems co-square well

finite square well

travelling wave soln,

transmission, reflection general properties of l D scatt. wave packet scattering

General Properties of 1-D bound states Parity

Landau & Lifsch. linear polynomial soln.

Linear Potential

gravity

Harmonic Oscillator: Hermite Poly.

Wave packets in the s.h.o. Classical limit of the Schr. eg.

wave fronts- optical analog WKB approximation

bound states in WKB tunneling in WKB

Free particles and small perturbations Formal discussion of operators in OM

Hermitian ops.

Unitary ops.

Orthog., completeness, etc. Physical interpretation of e.v .'s,

fluctuations, and measurement

Hilbert Space

adjoint space Hermitian spaces

mathematical postulates matrix representations commutators

Dirac Notation Degenerate solutions

Simultaneous efs.

Linear transf. in Hilbert Space General Solution of 2nd order eg.

solns as states in Hilbert Space continuous case

dispersionless case and e.v.'s Operator methods

raising-lowering  ops. coherent states of the h.o.

Transformation Theor:y

Dirac Notation meaning of symmetry Unitary transf.

Rotations Variations of fields

Commut. Rules for Rotations Physical  interp Hilbert space

..

Connection to Classical Physics canonical transf.

formal correspondence to QM

Pictures- Time Dependence Schroedinger picture Heisenberg picture

Green's functions-propagators

Periodic potentials Central Forces

center of mass coords

Angular mom. ops (class & qm)

Angular solutions sperica! harmonics

single-valuedness of solns radial wave fens.

spher. sq. well

spher. Bessel fens. Free Particle in spher. coords

2-Body Problem- deuteron Hydroeen Atom

Bound states energy levels operator soln

3-D harmonic oscillator vs .

H- atom

Time Independent Perturbation Thy 1st,2nd order R.S theory

B.W. Theory Degenerate pert .thy Helium atom

Stark effect

Variational  principles

gd. state of He.