Titlebook: Geometric Quantization and Quantum Mechanics; Jȩdrzej Śniatycki Book 1980 Springer-Verlag New York Inc. 1980 Quantenmechanik.Quantisierung

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Book 1980) and Simms and Woodhouse (1976) present the theory of geometric quantization and its relationship to quantum mech­ anics. The purpose of the present book is to complement the preceding ones by including new developments of the theory and emphasizing the computations leading to results in quantum me

Airtight

Introduction, a Hilbert space . of quantum states and defines a map . from a subset of the Poisson algebra to the space of symmetric operators on .. The domain of . consists of all “.-quantizable” functions. The definition of . requires some additional structure on the phase space. The functions which generate o

机警

任命

Representation Space,mplete set of commuting observables. In the process of quantization, however, one has only the classical phase space (X, ω) to work with, and one has to find a suitable classical counterpart of the notion of a complete set of commuting observables. A natural choice is a set of n = 1/2dim X functions

majestic

majestic

Other Representations,nctions gives rise to the Schrödinger representation. The momentum representation corresponds to the polarization spanned by the Hamiltonian vector fields of the momentum variables. The Blattner-Kostant-Sternberg kernel between these representations reduces to the Fourier transform. In this chapter,

传染

,Time-Dependent Schrödinger Equation,extended to evolution space yields an intrinsic quantum theory equivalent to that based on the time-dependent Schrödinger equation. We restrict our attention to the quantum mechanics of a single particle with a time-dependent potential.

Eulogy

Relativistic Dynamics in an Electromagnetic Field,re Y is the space-time manifold, Л: .Y → Y is the cotangent bundle projection, and .[cf. Sec. 2.3]. Assuming that Y is orientable, and following the reasoning of Sec. 7.2 leading to a metaplectic structure on (.Ydθ.), we obtain a metaplectic structure on (.Y,ω.). The vertical distribution D on .Y ta

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