目錄
Preface
1. A Brutal Fact of Life
1.1 Causality and determinism
1.2 Bell's inequality: No hidden determinism
1.3 Remarks on terminology
2. Kinematics: How Quantum Systems are Described
2.1 Stern–Gerlach experiment
2.2 Successive Stern–Gerlach measurements
2.3 Order matters
2.4 Mathematization
2.5 Probabilities and probability amplitudes
2.6 Quantum Zeno effect
2.7 Kets and bras
2.8 Brackets, bra-kets, and ket-bras
2.9 Pauli operators, Pauli matrices
2.10 Functions of Pauli operators
2.11 Eigenvalues, eigenkets, eigenbras
2.12 Wave-particle duality
2.13 Expectation value
2.14 Trace
2.15 Statistical operator
2.16 Mixtures and blends
2.17 Nonselective measurement
2.18 Entangled atom pairs
2.19 State reduction
2.20 Measurements with more than two outcomes
2.21 Unitary operators
2.22 Hermitian operators
3. Dynamics: How Quantum Systems Evolve
3.1 Schrdinger equation
3.2 Heisenberg equation
3.3 Equivalent Hamilton operators
3.4 von Neumann equation
3.5 Example: Larmor precession
3.6 Time-dependent probability amplitudes
3.7 Schrdinger equation for probability amplitudes
3.8 Time-independent Schrdinger equation
3.9 Example: Two magnetic silver atoms
4. Motion along the x Axis
4.1 Kets, bras, wave functions
4.2 Position operator
4.3 Momentum operator
4.4 Heisenberg's commutation relation
4.5 Position-momentum transformation function
4.6 Expectation values
4.7 Uncertainty relation
4.8 State of minimum uncertainty
4.9 Time dependence
4.10 Excursion into classical mechanics
4.11 Hamilton operator, Schrdinger equation
4.12 Time transformation function
5. Elementary Examples
5.1 Force-free motion
5.1.1 Time-transformation functions
5.1.2 "Spreading" of the wave function
5.1.3 Long-time and short-time behavior
5.1.4 Interlude: General position-dependent force
5.1.5 Energy eigenstates
5.2 Constant force
5.2.1 Energy eigenstates
5.2.2 Limit of no force
5.3 Harmonic oscillator
5.3.1 Energy eigenstates: Power-series method
5.3.2 Energy eigenstates: Ladder-operator approach
5.3.3 Hermite polynomials
5.3.4 Infinite matrices
5.4 Delta potential
5.4.1 Bound state
5.4.2 Scattering states
5.5 Square-well potential
5.5.1 Bound states
5.5.2 Delta potential as a limit
5.5.3 Scattering states. Tunneling
Index
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