A method of phase functions in Quantum mechanics

V.V. Babikov

Go. Torres-Vega, John H. Frederick

A recently proposed phase-space representation for quantum mechanics provides a formal means for investigating the correspondence between classical and quantum mechanics. To explore the implications of this new representation, we introduce a numerical method for propagating an initial wave function directly in phase space. We illustrate the usefulness of the proposed method by analyzing two simple quantum-mechanical systems in phase space.

V.V. Babikov

Marcos Mariño

This chapter presents Wigner’s approach to quantum mechanics, based on the Wigner function in phase space. It explains Wigner–Weyl quantization, which makes it possible to associate functions on phase space to wave functions and operators, and it develops the technology to do quantum mechanics in this formalism. This includes the star product, Moyal evolution, and star-eigenvalue equations. It also develops semiclassical methods in this formulation, and it has a section on Berry’s semiclassical formula for the Wigner function in one-dimensional systems.

Kohji KUMAKURA

P K Bera, T. Nandi, B. Talukdar

Methods of supersymmetric quantum mechanics (SUSYQM) are used to derive relations between phase functions which occur in the context of the variable-phase approach to potential scattering. It is shown that the phase-equivalent potentials obtained by the application of SUSYQM are not off-shell equivalent. A case study is presented in support of this.