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Lectures on Quantum Mechanics, Volume 2: Simple Systems Book

Lectures on Quantum Mechanics, Volume 2: Simple Systems
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Lectures on Quantum Mechanics, Volume 2: Simple Systems, , Lectures on Quantum Mechanics, Volume 2: Simple Systems
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  • Lectures on Quantum Mechanics, Volume 2: Simple Systems
  • Written by author Berthold-Georg Englert
  • Published by World Scientific Publishing Company, Incorporated, May 2006
  • The reader of Simple Systems is not expected to be familiar with the material in Basic Matters, but should have the minimal knowledge of a standard brief introduction to quantum mechanics with its typical emphasis on one-dimensional position wave function
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Preface     vii
Quantum Kinematics Reviewed     1
Schrodinger's wave function     1
Digression: Vectors, coordinates, and all that     3
Dirac's kets and bras     10
xp transformation function     16
Position operator, momentum operator, functions of them     20
Traces and statistical operators     24
Algebraic completeness of operators X and P     32
Weyl commutator, Baker-Campbell-Hausdorff relations     37
Quantum Dynamics Reviewed     41
Temporal evolution     41
Time transformation functions     49
Examples     53
Force-free motion     53
Time-dependent spreads     58
Uncertainty ellipse     60
Constant force     63
Time-dependent force     67
Harmonic oscillator     72
Ladder operators     78
Coherent states     84
Completeness of the coherent states     88
Fock states and coherent states     90
Time dependence     92
Two-dimensional harmonic oscillator     98
Isotropy     98
Eigenstates     102
Orbital AngularMomentum     107
Commutation relations     107
Eigenvalues and eigenstates     113
Differential operators. Polar coordinates     117
Differential operators. Spherical coordinates     120
Hydrogen-like Atoms     125
Hamilton operator, Schrodinger equation     125
Wave functions     129
Two-dimensional harmonic oscillator     129
Hydrogenic atoms     133
Approximation Methods     139
Hellmann-Feynman theorem     139
Virial theorem     142
Rayleigh-Ritz variational method     145
Rayleigh-Schrodinger perturbation theory     153
Brillouin-Wigner perturbation theory     159
Perturbation theory for degenerate states     164
Linear Stark effect     166
WKB approximation     172
Index     185


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