Hilbert Spaces, Wavelets, Generalised Functions and Modern Quantum Mechanics
Willi-Hans SteebMany excellent textbooks have been written on Hilbert space theory and linear operators in Hilbert spaces. Comprehensive surveys of this subject are given by Weidmann [68], Prugovecki [47], Yosida [69], Kato [31], Richtmyer [49], Sewell [54] and others. The theory of generalized functions is also well covered in good textbooks (Gelfand and Shilov [25], Vladimirov [67]. Furthermore, numerous textbooks on quantum mechanics exist (Dirac [17], Landau and Lifshitz [36], Messiah [41], Gasiorowicz [24], Schiff [51], Eder [18] and others). 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 mathematical background. The basic mathematical tools to understand quantum me- chanics should be fully integrated into an education in quantum mechanics.