Lectures on Quantum Mechanics, Volume 1: Basic Matters Book

Preface     vii
A Brutal Fact of Life     1
Causality and determinism     1
Bell's inequality: No hidden determinism     4
Remarks on terminology     8
Kinematics: How Quantum Systems are Described     11
Stern-Gerlach experiment     11
Successive Stern-Gerlach measurements     14
Order matters     17
Mathematization     17
Probabilities and probability amplitudes     23
Quantum Zeno effect     32
Kets and bras     35
Brackets, bra-kets, and ket-bras     38
Pauli operators, Pauli matrices     41
Functions of Pauli operators     44
Eigenvalues, eigenkets, eigenbras     46
Wave-particle duality     51
Expectation value     51
Trace     54
Statistical operator     56
Mixtures and blends     60
Nonselective measurement     61
Entangled atom pairs     63
State reduction     68
Measurements with more than two outcomes     70
Unitary operators     75
Hermitian operators     78
Dynamics: How Quantum Systems Evolve     81
Schrodinger equation     81
Heisenberg equation     85
Equivalent Hamilton operators     87
von Neumann equation     88
Example: Larmor precession     89
Time-dependent probability amplitudes     93
Schrodinger equation for probability amplitudes     94
Time-independent Schrodinger equation     98
Example: Two magnetic silver atoms     101
Motion along the x Axis     109
Kets, bras, wave functions     109
Position operator     114
Momentum operator     117
Heisenberg's commutation relation     119
Position-momentum transformation function     119
Expectation values     122
Uncertainty relation     125
State of minimum uncertainty     129
Time dependence     132
Excursion into classical mechanics     132
Hamilton operator, Schrodinger equation     136
Time transformation function     139
Elementary Examples     141
Force-free motion     141
Time-transformation functions     141
"Spreading" of the wave function     143
Long-time and short-time behavior      149
Interlude: General position-dependent force     155
Energy eigenstates     157
Constant force     160
Energy eigenstates     160
Limit of no force     162
Harmonic oscillator     165
Energy eigenstates: Power-series method     165
Energy eigenstates: Ladder-operator approach     170
Hermite polynomials     176
Infinite matrices     177
Delta potential     181
Bound state     181
Scattering states     186
Squre-well potential     191
Bound states     191
Delta potential as a limit     196
Scattering states. Tunneling     197
Index     203