Hilbert Spaces, Wavelets, Generalised Functions and Modern Quantum Mechanics
Springer (Verlag)
978-94-010-6241-1 (ISBN)
Besides these books there are several problem books on quantum mechanics (Fliigge [22], Constantinescu and Magyari [15], ter Haar [64], Mavromatis [39], Steeb [59], Steeb [60], Steeb [61]) and others). Computer algebra implementations of quantum mechanical problems are described by Steeb [59]. Unfortunately, many standard textbooks on quantum mechanics neglect the math- ematical background. The basic mathematical tools to understand quantum me- chanics should be fully integrated into an education in quantum mechanics.
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.
Reihe/Serie | Mathematics and Its Applications ; 451 | Mathematics and Its Applications ; 451 |
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Zusatzinfo | X, 238 p. |
Verlagsort | Dordrecht |
Sprache | englisch |
Maße | 160 x 240 mm |
Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
Mathematik / Informatik ► Mathematik ► Analysis | |
Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
Naturwissenschaften ► Physik / Astronomie ► Allgemeines / Lexika | |
Naturwissenschaften ► Physik / Astronomie ► Quantenphysik | |
Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik | |
ISBN-10 | 94-010-6241-2 / 9401062412 |
ISBN-13 | 978-94-010-6241-1 / 9789401062411 |
Zustand | Neuware |
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