论文标题
具有对称性凸电势的Schrödinger方程的病毒式侵略
Virial-ansätze for the Schrödinger Equation with a symmetric strictly convex potential
论文作者
论文摘要
考虑到对称的严格凸电势，可以从病毒定理中推断出局部关系，该关系可以基于可以构建实际对数符号函数。将其用作权重函数，并以仍然可以验证病毒定理的方式，为相关的Schrödinger方程的本征函数提供无参数的Ansätze。为了说明这一过程，该技术已成功地针对谐波振荡器进行了测试，该技术导致确切的本本函数，并针对四分之一的Anharmonic振荡器，该振荡器被认为是Schrödinger方程的新方法的范式测试地面。
Considering symmetric strictly convex potentials, a local relationship is inferred from the virial theorem, based on which a real log-concave function can be constructed. Using this as a weight function and in such a way that the virial theorem can still be verified, parameter-free ansätze for the eigenfunctions of the associated Schrödinger equation are built. To illustrate the process, the technique is successfully tested against the harmonic oscillator, in which it leads to the exact eigenfunctions, and against the quartic anharmonic oscillator, which is considered the paradigmatic testing ground for new approaches to the Schrödinger equation.
