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Invariants and Lie algebraic solutions of Schrödinger equation (1993)

Salmistraro, Franco ; Rosso, Riccardo

College Park, Md. : American Institute of Physics (AIP)

Journal of Mathematical Physics 34 (1993), S. 3964-3979

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ISSN: 1089-7658

Source: AIP Digital Archive

Topics: Mathematics , Physics

Notes: A representation of invariants in quantum mechanics for a general time-dependent Hamiltonian is provided. The main properties of these operators and their relevance for solving the Schrödinger equation are discussed in light of this representation. In particular, the well-known Lewis and Riesenfeld's method is shown to be recovered quite directly by the present approach. A detailed analysis is concerned with Hamiltonians which at each instant are elements of a finite dimensional Lie algebra. Exploiting the Wei and Norman's theory for such Hamiltonians, it is found that the evolution of a quantum system is always determined, in part or fully, by an invariant which belongs to the same algebra.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1063/1.530017

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