论文标题
量子力学中能量特征值问题的拉普拉斯方法
The Laplace method for energy eigenvalue problems in quantum mechanics
论文作者
论文摘要
量子力学具有大约十二个可解决的电位。通常，通过对结合态的通用串联解决方案（使用Froebenius方法），然后对连续态态（如果存在）来解决它们的时间无关的Schroedinger方程。在这项工作中，我们提出了一种基于拉普拉斯方法解决这些问题的替代方法。该技术使用类似的程序和连续状态使用类似的过程。它最初是由Schroedinger用于氢的波形时使用的。狄拉克也提倡使用这种方法。我们讨论为什么这是研究生学习和描述如何使用它来解决所有波形以汇合超测量功能表示的问题的强大方法。
Quantum mechanics has about a dozen exactly solvable potentials. Normally, the time-independent Schroedinger equation for them is solved by using a generalized series solution for the bound states (using the Froebenius 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 Schroedinger when he solved for the wavefunctions of hydrogen. Dirac advocated using this method too. We discuss why it is a powerful approach for graduate students to learn and describe how it can be employed to solve all problems whose wavefunctions are represented in terms of confluent hypergeometric functions.
