辅助场作为计算薛定谔方程解析解的工具
Auxiliary fields as a tool for computing analytical solutions of the Schrödinger equation
摘要：
本文提出了一种新的方法来获得具有任意势且具有束缚态的薛定谔方程的近似解。这种方法依赖于辅助场技术，在许多情况下可以找到解析解。它为研究任意势场中束缚态能谱的定性特征提供了一种方便的方法。特别地，我们通过求解幂律形式和对数形式的中心势来说明我们的方法。对于这些类型的势，我们提出了非常精确的解析能量公式，改进了许多可以在文献中找到的相应公式。
英文摘要：
We propose a new method to obtain approximate solutions for the Schrödinger equation with an arbitrary potential that possesses bound states. This method, relying on the auxiliary field technique, allows in many cases to find analytical solutions. It offers a convenient way to study the qualitative features of the energy spectrum of bound states in any potential. In particular, we illustrate our method by solving the case of central potentials with power-law form and with logarithmic form. For these types of potentials, we propose very accurate analytical energy formulae which improve a lot the corresponding formulae that can be found in literature.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
