Hilbert Spaces, Wavelets, Generalised Functions and Modern Quantum Mechanics

✍ Scribed by Willi-Hans Steeb (auth.)

• Publisher: Springer Netherlands
• Year: 1998
• Tongue: English
• Leaves: 246
• Series: Mathematics and Its Applications 451
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-x
Hilbert Spaces....Pages 1-16
Fourier Transform and Wavelets....Pages 17-30
Linear Operators in Hilbert Spaces....Pages 31-50
Generalized Functions....Pages 51-62
Classical Mechanics and Hamilton Systems....Pages 63-68
Postulates of Quantum Mechanics....Pages 69-76
Interaction Picture....Pages 77-84
Eigenvalue Problem....Pages 85-100
Spin Matrices and Kronecker Product....Pages 101-108
Parity and Group Theory....Pages 109-116
Uncertainty Relation....Pages 117-122
Harmonic Oscillator....Pages 123-134
Coherent and Squeezed States....Pages 135-140
Angular Momentum and Lie Algebras....Pages 141-148
Two-Body Bound State Problem....Pages 149-156
One-Dimensional Scattering....Pages 157-164
Solitons and Quantum Mechanics....Pages 165-170
Perturbation Theory....Pages 171-178
Helium Atom....Pages 179-182
Potential Scattering....Pages 183-188
Berry Phase....Pages 189-194
Measurement and Quantum States....Pages 195-204
Quantum Computing....Pages 205-216
Lebesgue Integration and Stieltjes Integral....Pages 217-224
Back Matter....Pages 225-238

✦ Subjects

Theoretical, Mathematical and Computational Physics;Quantum Physics;Applications of Mathematics;Functional Analysis;Linear and Multilinear Algebras, Matrix Theory