Lectures on Quantum Mechanics - Directory

1 LECTURE NOTES ON Quantum MECHANICSPHY 851/852 2020/2021/2022 Scott PrattDepartment of Physics and AstronomyMichigan State UniversityFORWARDT hese notes are for the two-semester graduate level Quantum Mechanics class taught at Michi-gan State University. Although they are more terse than a typical text book, they do cover allthe material used in PHY 851/852. The notes presume a familiarity with basic undergraduateconcepts in Quantum is welcome to use the notes to their heart s content, though the text should be treatedwith the usual academic respect when it comes to copying material.

2 If anyone is interested inthe LATEX source files, they should contact me Solutions to the end-of-chapterproblems will also be provided on the course web site, ~pratt/phy851. Please beware that this is a web manuscript, and is thus a living document and subjectto change at any States and .. Conjugate: .. Operators and Transformations .. Matrices .. of Two-Component Spin-Half Systems .. of Photons .. in Time .. of Two-component Systems.. Heisenberg and Schr dinger representations.

3 Uncertainty Relations .. Exercises ..202 Coordinate and Momentum dinger s Wave Equation .. States .. Charge Conservation and the Equation of Continuity .. Problems in One Dimension .. Packets .. Harmonic Oscillator .. , Green s Functions and Integral Equations .. Space Density and Wigner Functions .. Solving Schr dinger s Equation .. Combining Coordinate Space and Spin .. Exercises ..503 Charged Particles in Electromagnetic and Scalar Potentials .. Invariance.

4 With Uniform Magnetic Fields .. with Uniform Electric and Magnetic Fields .. Integrals and the Aharanov-Bohm Effect..614 Angular Momentum and Central Baker-Campbell-Hausdorff Relation .. Rotations .. Greatly Abbreviated Guide to Group Theory .. |~L|2 operator .. and Lowering Operators for Angular Momentum .. Harmonics .. Relative and Center-of-Mass Coordinates .. Oscillators in Cartesian Coordinates .. Solving the Radial Wave Equation for Spherically Symmetric Cases.

5 Spherical Harmonic Oscillator Spherical Basis.. The Hydrogen Atom .. Adding Angular Momentum .. Clebsch-Gordan Coefficients .. Exercises ..905 Symmetries and Conservation and Discrete Symmetries .. Reversal .. Reversal and Angular Momentum.. Particle in a Periodic Potential .. with Discrete Rotational Symmetry .. 1046 Approximation WKB Approximation .. Theory .. Sudden Approximation .. Perturbation Theory .. Perturbation Theory .. Interaction Representation (Picture).

6 Perturbation Theory .. s Golden Rule .. Perturbations .. An Exactly Solvable Model of a Time-Dependent Interaction .. Exercises .. 1247 Perturbative Approaches to Sections .. Born approximation .. Functions.. Factors .. Order Expansions .. (Time-Ordered Evolution Operators).. Fourier Transform of the Propagator, G( ).. to the Same State .. of a Particle in Medium .. Resonant Scattering .. Resonant Scattering, Simplified .. Exercises.

7 1478 Scattering at Lower Waves and Phase Shifts.. Optical Theorem .. Phase Shifts Numerically .. Low Energy Limit .. s Theorem .. Range Theory for`= 0.. Waves and Gamow Factors .. Interpretation of the Scattering Wave Function .. 1669 Second Quantization and Fields and Second Quantization .. Operators: Creation and Destruction Operators in Coordinate Space.. and the Hamiltonian .. with an External Potential .. Decays .. Dipole Approximation.

8 Dipole and Electric Quadrupole Radiation .. 18510 Advanced Topics in Angular Isospin .. Combining Three Angular Momenta .. Notation: Conventions for Clebsch-Gordan Coefficients and Wigner 3j or 6j Irreducible Tensor Operators.. WignerDmatrices .. The Two-Dimensional Analogy of the Wigner Eckart Theorem .. The Wigner Eckart Theorem .. Exercises .. 20411 The Spin Statistics Theorem .. The Pauli-Exclusion Principle .. Fermi Gases and Neutron Stars.

9 Multi-Particle Symmetrization and Slater Determinants .. Fermi Creation and Destruction Operators .. Fermionic Field Operators .. Exercises .. 22212 Non-Perturbative Approaches for Many-Fermion Interacting Fermi Systems Two and Four-Point Interactions .. The Thomas-Fermi Approximation .. The Hartree-Fock Approximation .. Hartree-Fock for Atoms .. The Periodic Table .. Configuration Splitting and Hund s Rules.. Constructing States According to Total~Land Total~S.

10 Permutation Symmetry .. Zeeman Effect and the Land gFactor .. and the Adiabatic Approximation .. Hydrogen Molecule and Pairing .. Pairs .. Gap .. Levels and the Integer Quantum Hall Effect .. 24613 Relativistic Quantum The Klein-Gordon Equation .. Current Conservation .. Coupling to the Electromagnetic Field .. The Dirac Equation.. Conserved Quantities .. Solutions for Free Particles .. Non-Relativistic Limit and thegFactor.