Integration of the Schroedinger equation by canonical transformations
Gin-yih Tsaur and Jyhpyng Wang
Physical Review A 65, 012104 (2001)
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 Schroedinger 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 Poeschl-Teller potential, the Hulthe´n potential, etc.
Institute of Atomic and Molecular Sciences Academia Sinica
