Lectures on Quantum Mechanics, Volume 3: Perturbed Evolution Book

Preface     vii
Basics of Kinematics and Dynamics     1
Brief review of basic kinematics     1
Bohr's principle of complementarity     7
Complementary observables     7
Algebraic completeness     13
Bohr's principle. Technical formulation     17
Composite degrees of freedom     17
The limit N to [infinity]. Symmetric case     19
The limit N to [infinity]. Asymmetric case     26
Bohr's principle. Quantum indeterminism     30
Brief review of basic dynamics     31
Equations of motion     31
Time transformation functions     33
Schwinger's quantum action principle     36
An example: Constant force     39
Insertion: Varying an exponential function     41
Time-independent Hamilton operator     43
Time-Dependent Perturbations     45
Born series     45
Scattering operator     48
Dyson series     50
Fermi's golden rule     52
Photon emission by a "two-level atom"     57
Golden-rule treatment     57
A more detailed treatment     60
An exact treatment     65
Driven two-level atom     68
Schrodinger equation     68
Resonant drive     71
Periodic drive     72
Very slow drive. Adiabatic evolution     74
Adiabatic population transfer     78
Equation of motion for the unitary evolution operator     81
Scattering     87
Probability density, probability current density     87
One-dimensional prelude: Forces scatter     91
Scattering by a localized potential     95
Golden-rule approximation     95
Example: Yukawa potential     100
Rutherford cross section as a limit     101
Lippmann-Schwinger equation     102
Born approximation     111
Transition operator     112
Optical theorem     114
Example of an exact solution     116
Partial waves     118
s-wave scattering     123
Angular Momentum     129
Spin     129
Addition of two angular momenta     134
Two spin-1/2 systems     137
Total angular momentum of an electron     138
External Magnetic Field     141
Electric charge in a magnetic field      141
Electron in a homogeneous magnetic field     148
Indistinguishable Particles     155
Indistinguishability     155
Bosons and fermions     157
Scattering of two indistinguishable particles     161
Two-electron atoms     165
Variational estimate for the ground state     165
Perturbative estimate for the first excited state     171
Self-consistent single-electron wave functions     173
A glimpse at many-electron atoms     175
Index     181