Titlebook: Hilbert Spaces, Wavelets, Generalised Functions and Modern Quantum Mechanics; Willi-Hans Steeb Book 1998 Springer Science+Business Media D

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Classical Mechanics and Hamilton Systems,In classical mechanics (Arnold [2]) we consider the phase space . where .. Here . is the number of particles, . are the momenta and . are the coordinates.

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Postulates of Quantum Mechanics,Quantum mechanics, as opposed to classical mechanics, gives a probabilistic description of nature. The probabilistic interpretation of measurement is contained in one of the standard postulates of quantum mechanics (Glimm and Jaffe [26], Prugovecki [47], Schommers [52]).

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Harmonic Oscillator,The Hamilton function of the . in one space dimension is given by

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Coherent and Squeezed States,In chapter 12 we introduced the Bose operators . and .†. In this chapter we study the spectrum of . This leads to the so-called . (Louisell [37]). We adopt the Dirac notation. Coherent states are applied to a wide variety of physical problems (Klauder and Skagerstam [32], Kowalski and Steeb [33]).

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Angular Momentum and Lie Algebras,In the classical case the . is given by . where x denotes the cross product. The components of L are given by . Introducing the quantization . yields . Furthermore we define

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