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Lectures on Quantum Physics and Application.pdf

November 7, 2009 · Filed Under Physics  · Tags: , ,

Author: Paul E. Dimotakis, California Institute of Technology, this ebook is about Quantum Physics and Application contains great deal of physics theories such as: classical mechanics, wave mechanics, Schrodinger Equations etc.

Contents:

  • CLASSICAL MECHANICS
    • The principle of stationary action [ Lagrangian ~ ballistic trajectory ~ one-dimensional harmonic oscillator ~ motion of gravitating pair ~ motion in two-dimensional potential ~ momentum ~ motion in an Electromagnetic field ]
    • Conservation laws [ Momentum ~ Energy ]
    • Hamiltonian
    • Poisson brackets and constants of the motion
    • The assumptions o f classical mechanics
  • WAVE MECHANICS
    • An interference experiment
    • Wave packets [ Fourier transform ~ Parseval's theorem ~ Expectation values ~ x. k operators ~ Localization ~ Minimum joint spread ~ Wave packets o f definite x, or k ~ Commuting operators & simultaneous localization ~ Localization In three dimensions ~ Wave packet motion. Phase & group velocity ~ Frequency & time ]
    • Energy and momentum [ Black body radiation ~ Photoelectric effect ~ Compton scattering ~ deBroglie thesis ~ Momentum and energy operators ]
    • Wave particle duality and the uncertainty principle
    • Summary and conclusions. The correspondence principle
  • THE SCHRODINGER EQUATION
    • Hermitian operators . Eigenfunctions & eigenvalues [ momentum ~ adjoint operator ~ real elgenvalues ~ orthogonal eigenfunctions ~ minimum/maximum expectat ton values ]
    • Superposition of eigenfunctions
    • Eigenfunction expansions. Completeness.
    • Hermitian operators and associated observables
    • The energy operator . Schrodinger equation. [ Time rate of change of an operator , Constants of the motion ~ Conservation of probability ]
  • QUANTUM BEHAVIOR IN ONE-DIMENSIONAL POTENTIALS
    • Matching Conditions [ Motion in a constant potential . Free particle behauvior ~ Scattering by a potential step ~ Scattering by a potential step of finite length ~ Tunneling ~ Bound states of a rectangular potential well ~ The Infinite potential well ]
    • Density of states [ Motion in one dimension ~ Periodic boundary conditions ~ Density of states in three dimensions ~ Fermi energy of conduction electrons in a metal ~ Field emission ~ Contact potentials ~ Paramagnetic behavior of metals ]
  • HARMONIC OSCILLATOR SYSTEMS
    • Eigenualues and eigenfunctions
    • Ladder operators
    • Harmonic oscillators in thermal equilibrium
    • systems of uncoupled harmonlc oscillators
    • systems of uncoupled harmonlc oscillators in thermal equilibrium
    • Quantum mechanics of a fluid. Phonons.
  • ORBITAL ANGULAR MOMENTUM
    • The two dimensional harmonic oscillator [ Circular quanta ~ Motion of a charged particle in a uniform magnetic field ]
    • Angular momentum in three dimensions [ Rotational spectra of diatomic molecules at low temperatures ]
    • The spherical harmonics
  • MOTION IN A CENTRAL POTENTIAL
    • Motion in a constant potential . Free particle motion in spherical coordinates
    • Bound states of the spherical potential well
    • Motion in an attractive Coulomb potential. Hydrogenic wavefunctions
    • Vibrational-Rotational of diatomic molecules [ Diatomic molecules in thermal equilibrium ~ Radiative transitions of diatomic molecules in thermal equilibrium ]
  • METHODS OF APPROXIMATION
    • Time-independent perturbation of non-degenerate states [ Polarizability of harmonically bound charge ~ Special techniques (auxiliary operators, sum rules) ~ Polarizability of hydrogen atom ground state ~ an improved perturbation expansion ]
    • Perturbation of nearly degenerate states
    • Perturbation of degenerate states [ The linear Stark effect ]
    • Time dependent perturbation theory [ First Born approximation ~ Impulsive start of a constant potential ~ Transition amplitude matrix ]
    • Unitarity and the conservation of probability
    • Transitions as a result of perturbations localized in time. The S-matrix. Response of a ground state charged particle harmonic oscillator to a Gaussian impulse electric field
    • Transitions as a result of harmonic perturbations Transitions to or from a continuum
    • The differential scattering cross section in the Born approximation Coulomb Scattering
    • Transitions and the super positions of pure energy states
    • An improved transition rate calculation
  • THE ELECTROMAGNETIC FIELD
    • The Hamiltonian
    • Transition to Quantum Mechanics
    • The Quantum Mechanical vector potential operator The ground state of the electromagnetic field
    • The electromagnetic field in thermal equilibrium . Black body radiation
    • The eigenstates of the electromagnetic field
    • Electromagnetic field momentum
    • The photon
    • Photons and wave particle duality
    • The angular momentum of the photon
    • The vector potential in terms of circular polarization
    • operators
    • Photon modes
  • SPIN
    • Total angular momentum operator
    • addition of angular momenta. Clebsch-Gordan coeffiecients
    • Spin of the electron
    • Spin 1/2 [Spinors and Pauli spin matrices ~ Rotation of Spin 1/2 States ~ Spin 1/2 wavefunctions ]
    • The spinning electron in a Coulomb field
    • Relativistic corrections to the kinetic energy
  • INTERACTION OF RADIATION AND MATTER. EMISSION aND ABSORPTION
    • The Hamiltonian
    • The uperturbed Hamiltonian and eigenstates
    • Radiation transitions in the weak field approximation
    • The long wavelength approximation
    • Spontaneous lifetime of charged particles in an excited state. Rate of spontaneous emission from an excited hydrogen atom in the 2p state
    • Induced absorption and emission Particle transitions as a result of diffuse Cavity radiation
    • Electric multipole transition selection rules
    • Magnetic radiative transitions

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Download free Lectures on Quantum Physics and Application.pdf (427 pages pdf file, 20.6 MB).

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