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This book gives a comprehensive introduction to modern quantum mechanics, emphasising the underlying Hilbert space theory and generalised function theory. All the major modern techniques and approaches used in quantum mechanics are introduced, such as Berry phase, coherent and squeezed states, quantum computing, solitons and quantum mechanics.
Audience: The book is suitable for graduate students in physics and mathematics.
This book provides an introduction to Hilbert space theory, Fourier transform and wavelets, linear operators, generalized functions and quantum mechanics. Although quantum mechanics has been developed between 1925 and 1930 in the last twenty years a large number of new aspect and techniques have been introduced. The book also covers these new fields in quantum mechanics.
In quantum mechanics the basic mathematical tools are the theory of Hilbert spaces, the theory of linear operators, the theory of generalized functions and Lebesgue integration theory.
Unfortunately, many standard textbooks on quantum mechanics neglect the mathematical background. The basic mathematical tools to understand quantum mechanics should be fully integrated into an education in quantum mechanics.
Hilbert Spaces
Fourier Transform and Wavelets
Linear Operators in Hilbert Spaces
Generalized Functions
Classical Mechanics and Hamilton Systems
Postulates of Quantum Mechanics
Interaction Picture
Eigenvalue Problem
Spin Matrices and Kronecker Product
Parity and Group Theory
Uncertainty Relation
Harmonic Oscillator
Coherent and Squeezed States
Angular Momentum and Lie Algebras
Two-Body Bound State Problem
One-Dimensional Scattering
Solitons and Quantum Mechanics
Perturbation Theory
Helium Atom
Potential Scattering
Berry Phase
Measurement and Quantum States
Quantum Computing
Lebesgue Integration and Stieltjes Integral
Bibliography
Index