Quantum Mechanics: Fundamental Principles and Applications

✍ Scribed by John F. Dawson

• Year: 2009
• Tongue: English
• Leaves: 435
• Category: Library

✦ Synopsis

Great introduction to algebraic methods of quantum physics. Posted on the web by the author.

✦ Table of Contents

Linear algebra
Linear vector spaces
Linear independence
Inner product
The dual space
Non-orthogonal basis sets
Operators
Eigenvalues and eigenvectors:
Non-orthogonal basis vectors
Projection operators:
Spectral representations:
Basis transformations
Commuting operators
Maximal sets of commuting operators
Infinite dimensional spaces
Translation of the coordinate system
Measurement
The uncertainty relation
Time in non-relativistic quantum mechanics
Canonical quantization
Classical mechanics review
Symmetries of the action
Galilean transformations
Canonical quantization postulates
The Heisenberg picture
The Schrodinger picture
Canonical transformations
Schwinger’s transformation theory
Path integrals
Space-time paths
Some path integrals
Matrix elements of coordinate
Generating functionals

Closed time path integrals
Initial value conditions
Connected Green functions
Classical expansion
Some useful integrals
In and Out states
The interaction representation
The time development operator
Forced oscillator
Density matrix formalism
Classical theory
Classical time development operator
Classical averages
Classical correlation and Green functions
Classical generating functional
Quantum theory
Thermal densities
The canonical ensemble
Ensemble averages
Imaginary time formalism
Thermal Green functions
Path integral representation
Thermovariable methods
Green functions
Identical particles
Coordinate representation
Occupation number representation
Particle fields
Hamiltonian
Symmetries
Galilean transformations
The Galilean group
Group structure
Galilean transformations
Phase factors for the Galilean group
Unitary transformations of the generators
Commutation relations of the generators
Center of mass operator
Casimir invariants
Extension of the Galilean group
Finite dimensional representations
The massless case
Time translations
Space translations and boosts
Rotations
The rotation operator
Supersymmetry
Grassmann variables
Superspace and the D-N supersymmetry group
D-N supersymmetry transformations in quantum mechanics
Supersymmetric generators
R-symmetry
Extension of the supersymmetry group
Differential forms
Rotations of the basis sets
General Galilean transformations
Improper transformations
Parity
Time reversal
Charge conjugation
Scale and conformal transformations
Scale transformations
Conformal transformations
Wave equations
Scalars
Spinors
Spinor particles
Spinor antiparticles
Vectors
Massless wave equations
Massless scalers
Massless vectors
Finite quantum systems
Diatomic molecules
Periodic chains
Linear chains
Impurities
Bound state
Scattering One and two dimensional wave mechanics
Introduction
Transmission of a barrier
Wave packet propagation
Time delays for reflection by a potential step