Solvable Models in Quantum Mechanics

I The One-Center Point Interaction.- I.1 The One-Center Point Interaction in Three Dimensions.- I.2 Coulomb Plus One-Center Point Interaction in Three Dimensions.- I.3 The One-Center ?-Interaction in One Dimension.- I.4 The One-Center ??-Interaction in One Dimension.- I.5 The One-Center Point Interaction in Two Dimensions.- II Point Interactions with a Finite Number of Centers.- II.1 Finitely Many Point Interactions in Three Dimensions.- II.2 Finitely Many ?-Interactions in One Dimension.- II.3 Finitely Many ??-Interactions in One Dimension.- II.4 Finitely Many Point Interactions in Two Dimensions.- III Point Interactions with Infinitely Many Centers.- III.1 Infinitely Many Point Interactions in Three Dimensions.- III.2 Infinitely Many ?-Interactions in One Dimension.- III.3 Infinitely Many ??-Interactions in One Dimension.- III.4 Infinitely Many Point Interactions in Two Dimensions.- III.5 Random Hamiltonians with Point Interactions.- Appendices.- A Self-Adjoint Extensions of Symmetric Operators.- B Spectral Properties of Hamiltonians Defined as Quadratic Forms.- C Schrödinger Operators with Interactions Concentrated Around Infinitely Many Centers.- D Boundary Conditions for Schrödinger Operators on (0, ?).- E Time-Dependent Scattering Theory for Point Interactions.- F Dirichlet Forms for Point Interactions.- G Point Interactions and Scales of Hilbert Spaces.- H Nonstandard Analysis and Point Interactions.- H.1 A Very Short Introduction to Nonstandard Analysis.- H.2 Point Interactions Using Nonstandard Analysis.- I Elements of Probability Theory.- J Relativistic Point Interactions in One Dimension.- References.