Hilbert Spaces, Wavelets, Generalised Functions and Modern Quantum Mechanics

Inhaltsverzeichnis

• 1 Hilbert Spaces.
• 2 Fourier Transform and Wavelets.
• 3 Linear Operators in Hilbert Spaces.
• 4 Generalized Functions.
• 5 Classical Mechanics and Hamilton Systems.
• 6 Postulates of Quantum Mechanics.
• 7 Interaction Picture.
• 8 Eigenvalue Problem.
• 8.1 Eigenvalue Equation.
• 8.2 Applications.
• 9 Spin Matrices and Kronecker Product.
• 10 Parity and Group Theory.
• 11 Uncertainty Relation.
• 12 Harmonic Oscillator.
• 12.1 Classical Case.
• 12.2 Quantum Case.
• 13 Coherent and Squeezed States.
• 14 Angular Momentum and Lie Algebras.
• 15 Two-Body Bound State Problem.
• 15.1 Introduction.
• 15.2 Spherical Oscillator.
• 15.3 Hydrogen-like Atoms.
• 16 One-Dimensional Scattering.
• 17 Solitons and Quantum Mechanics.
• 18 Perturbation Theory.
• 19 Helium Atom.
• 20 Potential Scattering.
• 21 Berry Phase.
• 22 Measurement and Quantum States.
• 22.1 Introduction.
• 22.2 Measurement Problem.
• 22.3 Copenhagen Interpretation.
• 22.4 Hidden Variable Theories.
• 22.5 Everett Interpretation.
• 22.6 Basis Degeneracy Problem.
• 23 Quantum Computing.
• 23.1 Introduction.
• 23.2 Quantum Bit.
• 23.3 Quantum Gates.
• 23.4 Quantum Copying.
• 23.5 Shor’s Algorithm.
• 24 Lebesgue Integration and Stieltjes Integral.