期刊
JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS
卷 3, 期 4, 页码 367-398出版社
SPRINGER BASEL AG
DOI: 10.1007/s11868-012-0054-9
关键词
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资金
- Austrian Research Agency FWF [P 23902-N13]
- Portuguese Science Foundation (FCT) [PDTC/MAT/69635/2006, PTDC/MAT/099880/2008]
We present a phase space formulation of quantum mechanics in the Schrodinger representation and derive the associated Weyl pseudo-differential calculus. We prove that the resulting theory is unitarily equivalent to the standard configuration space formulation and show that it allows for a uniform treatment of both pure and mixed quantum states. In the second part of the paper we determine the unitary transformation (and its infinitesimal generator) that maps the phase space Schrodinger representation into another (called Moyal) representation, where the wave function is the cross-Wigner function familiar from deformation quantization. Some features of this representation are studied, namely the associated pseudo-differential calculus and the main spectral and dynamical results. Finally, the relation with deformation quantization is discussed.
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