**Texts:**

*Introductory Quantum Mechanics**, *by Richard L. Liboff, (QC 174.12 .L52 2003)*Quantum Chemistry**, *by Donald A. McQuarrie, (QD 462 .M4 1983)*Lectures on Quantum Mechanics**, *by Gordon Baym, (QC 174.1.B35)

If you buy only one book for this course, the Liboff text is probably the most useful.

**Other Useful Texts:**

- I
*ntroduction to Quantum Mechanics in Chemistry*, by Mark Ratner and George Schatz, (QD 462.R28 2000) *Mathematical Methods in the Physical Sciences*, by Mary L. Boas, (QA 37.B662)*Quantum Chemistry*, by Ira N. Levine (QD 462.L48 1991b)*Quantum Mechanics*, by Claude Cohen-Tannoudji, Bernard Dui, Frank Laloe, (QC 174.12.C6313)*Introduction to Quantum Mechanics*, by B.H. Bransden, C.J. Joachain, (QC 174.12 .B74 1989)*Quantum Mechanics*, by Eugen Merzbacher, (QC 174.1 .M577 1970*Quantum Theory,*by David Bohm, (QC 174.1.B634)*Advanced Quantum Mechanics,*by J. J. Sakurai, (QC 174.1.S158 1973)*Quantum Mechanics*, by L. D. Landau, (QC 174.1.L253)*Practical Quantum Mechanics*, by Siegfried Flugge, (QC 174.1 .F5713)*Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory*, by Attila Szabo, Neil S. Ostlund, (QD 462.S95 1989)

**Course Outline:**

**Brief Mathematical Review**(Liboff: Ch. 1 and Secs. 4.3 & 11.2, also Boas if you can find a copy)- Coordinate systems
- Ordinary Differential Equations
- Complex numbers, integration, and Cauchy's theorem
- Notational conventions - Dirac's Bra-ket notation
- Matrices, vectors, eigenvalues, eigenvectors, determinants, and traces

**The SchrÃ¶dinger Equation**(McQuarrie: Chapter 3)- Time-dependent
- Time-independent
- Linear Operators
- Particle in a one-dimensional box

**Postulates & Theorems**(Liboff: Chapters 3 & 4)- The state of the system is given by the wavefunction.
- Observables in Classical Mechanics correspond to operators in QM.
- QM observables will be measured at the eigenvalues of the operators.
- Averages of Quantum observables are obtained from expectation values.
- Time-dependence is derived from time-dependent SchrÃ¶dinger equation.
- QM operators are linear Hermitian operators.
- Eigenfunctions of Hermitian operators are orthogonal.
- Many operators to not commute.
- The Schwarz inequality and the uncertainty principle.

**The Harmonic Oscillator**(Liboff: 7.2, 7.3, Baym: pp. 123-128)- Differential Equations
- Raising & Lowering operators
- Applications to Spectroscopy

**Angular Momentum**(Liboff: Sections 9.1, 9.2, 9.3, Baym: Chapter 6)- Seperability
- The Laplacian in Spherical Coordinates
- The Rigid Rotator
- Spherical Harmonics
- Commutation of Angular Momentum operators

**The Hydrogen Atom**(Baym: Chapter 7, Liboff: Sections 10.5, 10.6)- Radial functions
- Angular functions
- High-Z hydrogenic atoms

**Approximate Methods**(Baym: Chapter 11, McQuarrie: Sections 7.4-7.7, Liboff: Chapter 13)- Perturbation Theory
- Derivation of the Van der Waals Interaction

- The Variational Method

- Perturbation Theory
**Quantum Scattering**(Liboff: Sections 7.5, 7.6, 7.7, 7.10)- Transmission through Potential Steps & Barriers
- Airy functions & the WKB Approximation

**Quantum Statistical Mechanics**(Liboff: Chapter 11)- Partition Functions
- The Density Matrix