量子力学中能量本征值问题的拉普拉斯方法

Q2 Physics and Astronomy
J. Canfield, A. Galler, J. Freericks
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引用次数: 0

摘要

量子力学大约有十几个完全可解的势。通常,它们的时间无关的薛定谔方程是通过使用束缚态的广义级数解(使用Fröbenius方法)和连续态的解析延拓(如果存在)来求解的。在这项工作中,我们提出了一种解决这些问题的替代方法,基于拉普拉斯方法。该技术对束缚态和连续态使用了类似的过程。它最初是薛定谔在求解氢的波函数时使用的。狄拉克也提倡使用这种方法。我们讨论了为什么它是一种强大的方法来解决所有波函数用合流超几何函数表示的问题,特别是对于连续体解,它可以通过易于编程的轮廓积分来确定。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The Laplace Method for Energy Eigenvalue Problems in Quantum Mechanics
Quantum mechanics has about a dozen exactly solvable potentials. Normally, the time-independent Schrödinger equation for them is solved by using a generalized series solution for the bound states (using the Fröbenius method) and then an analytic continuation for the continuum states (if present). In this work, we present an alternative way to solve these problems, based on the Laplace method. This technique uses a similar procedure for the bound states and for the continuum states. It was originally used by Schrödinger when he solved the wave functions of hydrogen. Dirac advocated using this method too. We discuss why it is a powerful approach to solve all problems whose wave functions are represented in terms of confluent hypergeometric functions, especially for the continuum solutions, which can be determined by an easy-to-program contour integral.
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来源期刊
Quantum Reports
Quantum Reports Physics and Astronomy-Physics and Astronomy (miscellaneous)
CiteScore
3.30
自引率
0.00%
发文量
33
审稿时长
10 weeks
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