The course is intended as an introduction to the methods of Quantum Mechanics. It will be assumed that the student has already some familiarity with ordinary and partial differential equations, linear algebra and Fourier transforms. Third-year courses in Electromagnetism and Classical Mechanics are prerequisites. Topics to be covered during the fall quarter will include:
∑Historical Retrospective. Black Body Radiation. Bohrís Atom and the Old Quantum Theory. De Broglie Waves. Double Slit Diffraction of Electrons. Wave Packets. Fourier Amplitudes. Group Velocity vs. Phase Velocity. Uncertainty Relations for a Wave Packet.
∑Schrödingerís Wave Equation. Free Particle. Dirac Delta Function. Probabilistic Interpretation of the Wavefunction. Normalization Condition. Probabilty Current. Expectation Values, Operators. Fundamental Commutator. Wave Equation for Stationary States. Time Evolution. Simple One-dimensional Applications. Expansion in Eigenfunctions, Completeness.
∑One-Dimensional Barrier Problems. Potential Step. Finite Depth Square Well. Bound States, Parity. Transmission and Reflection Coefficients. Potential Barrier. Tunneling. Examples of Tunneling in Metals and Nuclei.
∑Wavefunctions as States. Linear Operators in Hilbert Space. Hermitean Matrices and Operators. Examples. Derivation of the Heisenberg Uncertainty Relations.
∑Harmonic Oscillator. Power Series Solution. Eigenvalues and Eigenfunctions. Hermite Polynomials. Correspondence Principle. Matrix Mechanics of the Harmonic Oscillator.
Introduction to Quantum Mechanics, by R. Liboff (Addison Wesley, 1997);
Quantum Physics, by S. Gasiorowicz (Wiley, 1997).
Herbert W. Hamber, FRH 3172 (x5596).