TY - JOUR

T1 - Integration of the Schrödinger equation by canonical transformations

AU - Tsaur, Gin yih

AU - Wang, Jyhpyng

PY - 2002

Y1 - 2002

N2 - Owing to the operator nature of the quantum dynamical variables, classical canonical transformations for integrating the equations of motion cannot be extended to the quantum domain. In this paper, a general procedure is developed to construct the sequences of quantum canonical transformations for integrating the Schrödinger equations. The sequence is made of three elementary canonical transformations that constitute a much larger class than the unitary transformations. In conjunction with the procedure, we also developed a factorization technique that is analogous to the method of integration factor in classical integration. For demonstration, with the same procedure we integrate nine nontrivial models, including the centripetal barrier potential, the Kratzer’s molecular potential, the Morse potential, the Pöschl-Teller potential, the Hulthén potential, etc.

AB - Owing to the operator nature of the quantum dynamical variables, classical canonical transformations for integrating the equations of motion cannot be extended to the quantum domain. In this paper, a general procedure is developed to construct the sequences of quantum canonical transformations for integrating the Schrödinger equations. The sequence is made of three elementary canonical transformations that constitute a much larger class than the unitary transformations. In conjunction with the procedure, we also developed a factorization technique that is analogous to the method of integration factor in classical integration. For demonstration, with the same procedure we integrate nine nontrivial models, including the centripetal barrier potential, the Kratzer’s molecular potential, the Morse potential, the Pöschl-Teller potential, the Hulthén potential, etc.

UR - http://www.scopus.com/inward/record.url?scp=84891935863&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.65.012104

DO - 10.1103/PhysRevA.65.012104

M3 - 期刊論文

AN - SCOPUS:84891935863

SN - 1050-2947

VL - 65

SP - 7

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

IS - 1

ER -