The Schrdinger Equation [Paperback]

1. General Concepts of Quantum Mechanics.- 1.1. Formulation of Basic Postulates.- 1.2. Some Corollaries of the Basic Postulates.- 1.3. Time Differentiation of Observables.- 1.4. Quantization.- 1.5. The Uncertainty Relations and Simultaneous Measurability of Physical Quantities.- 1.6. The Free Particle in Three-Dimensional Space.- 1.7. Particles with Spin.- 1.8. Harmonic Oscillator.- 1.9. Identical Particles.- 1.10. Second Quantization.- 2. The One-Dimensional Schr?dinger Equation.- 2.1. Self-Adjointness.- 2.2. An Estimate of the Growth of Generalized Eigenfunctions.- 2.3. The Schr?dinger Operator with Increasing Potential.- 1. Discreteness of spectrum.- 2. Comparison theorems and the behaviour of eigenfunctions as x ??..- 3. Theorems on zeros of eigenfunctions.- 2.4. On the Asymptotic Behaviour of Solutions of Certain Second-Order Differential Equations as x ??.- 1. The case of integrable potential.- 2. Liouvilles transformation and operators with non-integrable potential.- 2.5. On Discrete Energy Levels of an Operator with Semi-Bounded Potential.- 1 The operator in a half-axis with Dirichlets boundary condition.- 2. The case of an operator on the half-axis with the Neumann boundary condition.- 3. The case of an operator on the whole axis.- 2.6. Eigenfunction Expansion for Operators with Decaying Potentials...- 1. Preliminary remarks.- 2. Formulation of the main theorem.- 3. Two proofs of Theorem 6.1..- 4. One-dimensional oper-ator obtained from the radially symmetric three-dimensional operator.- 5. The case of an operator on the whole axis.- 2.7. The Inverse Problem of Scattering Theory.- 1. Inverse problem on the half-axis.- 2. Inverse problem on the whole axis.- 2.8. Operator with Periodic Potential.- 1. Bloch functions and the band structure of the spectrum.- 2. Expansion into Bloch eigenfunctions.- 3. The density of states.- 3. The Multidimensional Schr?dinger Equation.- 3.1. Self-Adjointness.- 3.2. An Estimate of the Generalized Eigenfunctions.- 3.3. Discretló„