Introduction to Quantum Mechanics (ePub)

This text on quantum mechanics begins by covering all the main topics of an introduction to the subject. It then concentrates on newer developments. In particular it continues with the perturbative solution of the Schrödinger equation for various potentials and thereafter with the introduction and evaluation of their path integral counterparts. Considerations of the large order behavior of the perturbation expansions show that in most applications these are asymptotic expansions. The parallel consideration of path integrals requires the evaluation of these around periodic classical configurations, the fluctuation equations about which lead back to specific wave equations. The period of the classical configurations is related to temperature, and permits transitions to the thermal domain to be classified as phase transitions.In this second edition of the text important applications and numerous examples have been added. In particular, the chapter on the Coulomb potential has been extended to include an introduction to chemical bonds, the chapter on periodic potentials has been supplemented by a section on the band theory of metals and semiconductors, and in the chapter on large order behavior a section has been added illustrating the success of converging factors in the evaluation of asymptotic expansions. Detailed calculations permit the reader to follow every step.Contents:IntroductionHamiltonian MechanicsMathematical Foundations of Quantum MechanicsDirac's Ket- and Bra-FormalismSchrödinger Equation and Liouville EquationQuantum Mechanics of the Harmonic OscillatorGreen's FunctionsTime-Independent Perturbation TheoryThe Density Matrix and Polarization PhenomenaQuantum Theory: The General FormalismThe Coulomb InteractionQuantum Mechanical TunnelingLinear PotentialsClassical Limit and WKB MethodPower PotentialsScreened Coulomb PotentialsPeriodic PotentialsAnharmonic Oscillator PotentialsSingular PotentialsLarge Order Behavior of Perturbation ExpansionsThe Path Integral FormalismClassical Field ConfigurationsPath Integrals and InstantonsPath Integrals and Bounces on a LinePeriodic Classical ConfigurationsPath Integrals and Periodic Classical ConfigurationsQuantization of Systems with ConstraintsThe Quantum-Classical Crossover as Phase TransitionSummarizing RemarksReadership: Undergraduates and graduate students in physics; researchers in mathematical and particle physics.