摘要： Solvable models of the Schrödinger equation are important models of quantum systems because they are idealistic approximations of real quantum systems and much insight into real quantum systems can be gained from the exact solutions of the solvable models. In this paper we show that a universal Laplace transform scheme can be used to solve the Schrödinger equations in closed form for all known solvable models. The work demonstrates how to apply the Laplace transform to differential equations with non-constant coefficients, which is useful in many branches of physics in addition to quantum mechanics. The advantages of the Laplace transform over the power expansion method and its connection with the methods of supersymmetry shape-invariant potentials and quantum canonical transformation, which also give closed-form solutions for solvable models, are elucidated. 其他題名： EJP 其他題名： Eur. J. Phys 出版者： IOP Publishing 出版日期： 2014-01-01 出處： European journal of physics, 2014-01, Vol.35 (1), p.15006-17 資源來源： Institute of Physics Journals 版權： 2014 IOP Publishing Ltd 識別號： ISSN: 0143-0807 識別號： EISSN: 1361-6404 識別號： DOI: 10.1088/0143-0807/35/1/015006 識別號： CODEN: EJPHD4
