QUANTUM MECHANICS I - IIIPHYS 516 - 518Jan 1 - Dec. 31, 2010Prof. R. Gilmore12-918 [email protected] Schedule: MWF 11:00 - 11:50, Stratton 219Objective: To provide the foundations for modern physics.Two texts and one supplement will be used for this course. The first texthas been chosen from among many admirable texts because it provides a morecomprehensive treatment of quantum physics discovered since 1970 than othertexts.The second text will be used primarily during the second quarter of thiscourse (PHYS517). It provides hands-on experience for solving binding andscattering problems in one dimension and potentials involving periodic poten-tials, again in one dimension.The third text (optional) is strongly recommended for those who feel theirundergratuate experience in this beautiful subject may be deficient in some way.It is out of print but a limited number of copies are often available throughAmazon in the event out book store has sold out of their reprinted copies.L. E. BallentineQuantum MechanicsEnglewood Cliffs, NJ: Prentice Hall, 1990 ISBN 0-13-747932-8R. GilmoreElementary Quantum Mechanics in One DimensionBaltimore, Johns Hopkins University Press, 2004 ISBN 0-8018-8015-7R. H. Dicke and J. P. WittkeIntroduction to Quantum MechanicsReading, MA: Addison-Wesley, 1960 ISBN 0-?1Course Topics• Schr¨odinger’s Papers1. Quantization as an Eigenvalue Problem: Part I2. Quantization as an Eigenvalue Problem: Part II3. Quantization as an Eigenvalue Problem: Part III4. Quantization as an Eigenvalue Problem: Part IV• Forms of Quantum Theory: Matrix Mechanics, Wave Mechanics, PathIntegrals• Separation of Variables:1. Klein-Gordan Equation2. Schr¨odinger Equation• Frobenius’s Method• Eigenvalues and Eigenvectors• Brief Remarks: Spherical Harmonics• Time-Independent Perturbation Theory• Applictions:1. Finite nuclear size2. Zeeman Effect3. Stark Effect4. Crossed Fields• Harmonic Oscillator1. Analytic solution: Frobenius’ Method2. Operator solution3. Discretization and Matrix Diagonalization4. Ginzburg-Landau Quartic Potential• Coupled Oscillators1. Linear Molecules and Normal Modes2. One-Dimensional Solids2(a) One atom/unit cell(b) Two atoms/unit cell(c) Three atoms/unit cell3. Two-dimensional solids4. Three-dimensional solids• Electromagnetic Field1. Maxwell’s Equations2. Vector and Scalar Potentials3. Normal Modes4. Independent Oscillators5. Quantization• Time Dependence• Time-dependent perturbation theory• Representations:1. Schr¨odinger2. Interaction3. Heisenberg• Applictions:1. Perturbed harmonic oscillator2. Fermi golden Rule3. Lorentzians• Angular Momentum1. Analytic representation, angular variables: L2. Algebraic representation, |l, mli3. J ' a†a4. Spin angular momentum: S5. Total angular momentum: J6. Spherical harmonics7. Clebsch-Gordan coefficients• Angular Momentum Applications1. Shielded Coulomb Potential → Mendelyeev2. Harmonic + Square Well + Spin Orbit = Nuclear Shell Model3. Hydrogen → Positronium → Charmonium →