Preface
Chapter 1 Quantum states and physical quantities
1.1 Quantum states as linear vectors in Hilbert space
1.1.1 Quantum states as linear vectors
1.1.2 Axiom of quantum mechanics concerning quantum states
1.2 Physical quantities as operators in Hilbert space
1.2.1 Eigenvalue and eigenvector of Hermitian operator
1.2.2 Orthogonal-normalization condition of eigenvectors
1.2.3 Axiom of quantum mechanics concerning physical quantities
1.2.4 Completeness condition of eigenvector system
1.2.5 Projection operator
1.2.6 Density operator Pure state and mixed state
1.3 Representation
1.3.1 Definition of representation
1.3.2 Representation transformation
1.3.3 Enter in and escape from a representation
1.3.4 Invariances of representation transformation
1.4 Operators as non-commuting quantities
1.4.1 Simultaneous measurability of physical quantities
1.4.2 Commutator algebra
1.4.3 Function of operator
1.5 Unitary transformation Generator of continuous transformation
1.5.1 Similar transformation and unitary transformation
1.5.2 Relation between unitary operator and Hermitian operator
1.5.3 Continuous transformation Generator
1.5.4 Space displacement Momentum
1.5.5 Space rotation Angular momentum
Chapter 2 Time evolution of microscopic system SchrSdinger equation and propagator
2.1 Time evolution in coordinate representation
2.2 Time evolution operator in Hilbert space
2.3 Picture in quantum mechanics
2.3.1 Definition of picture and picture-transform in quantum mechanics
2.3.2 SchrSdinger picture and Heisenberg picture
2.3.3 Interaction picture
2.4 Time evolution in the form of path integral
2.4.1 Functional integral formula for propagator
2.4.2 Functional integral as limit of multiple-integral
2.4.3 Functional integral as sum over path
2.4.4 Path-integral of Gaussian type
2.4.5 From path integral to SchrSdinger equation
2.5 Diffraction phenomena in quantum mechanics
2.5.1 The role of phase in quantum mechanics
2.5.2 Double-slot diffraction
2.5.3 Aharonov-Bohm effect Magnetic-flux quantum
2.6 Symmetry of microscopic system and conservation of physical quantity
2.6.1 Symmetry of microscopic system
2.6.2 Conservation of physical quantity
2.6.3 Parity
2.6.4 Time reversal
Chapter 3 Angular momentum
3.1 General solution of the eigenvalue problem of angular momentum
3.1.1 The procedure for solving eigenvalue problem directly in Hilbert space
3.1.2 Solution of the eigenvalue problem of angular momentum
3.2 Two kinds of angular momentum
3.2.1 Orbital angular momentum
3.2.2 Spin
3.3 Spin 1/2
3.3.1 Properties of Pauli matrix
3.3.2 Density matrix of spin 1/2 state Polarization vector
3.4 Representation of angular momentum
3.4.1 Reducible and irreducible representations
3.4.2 Irreducible tensor operator
3.4.3 Property of D function
3.5 Addition of angular momentum Clebsch-Gordan coefficients
3.5.1 Addition of angular momentum
3.5,2 Clebsch-Gordan coefficients
3.5.3 Addition of D function
Chapter 4 Multi-particle system
4.1 Axiom on indistinguishability of identical particles
4.2 Fock representation of multi-particle state -- Discrete spectrum
4.2.1 The representation basis
4.2.2 Basic operators
4.2.3 Action of basic operators on representation basis
4.2.4 Representation- and canonical-transformations of annihilation and creation operators
4.2.5 Operators of physical quantities in multi-particle system
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Chapter 5 Uncertainty relation Coherent state
Chapter 6 One-dimensional problem
Chapter 7 Three-dimensional Scattering
Chapter 8 Relativistic quantum mechanics
Hnts to Selected Exercises
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