论文标题
六振荡器的Schrödinger方程的HERMITE功能解决方案
Hermite function solutions of the Schrödinger equation for the sextic oscillator
论文作者
论文摘要
我们检查了可以根据Hermite函数扩展六边形的Anharmonic振荡器的径向固定schrödinger方程的解决方案。我们发现，这对于由参数设定了离心屏障强度区分的电势的无限层次结构是可能的。层次结构的$ n $''涉及$ n $的$ n $解决方案通常不同的能源值。对于层次结构的特定成员来说，存在着无限的许多绑定状态，具有正方形的整合波函数，它是根据Hermite函数编写的，这些函数在原点和无穷大范围内消失了。这些结合状态对应于参数设定谐波项的强度的不同值。我们还研究了与从准溶解电势的形式主义获得的六振荡器的多项式溶液的联系。
We examine the conditions under which the solution of the radial stationary Schrödinger equation for the sextic anharmonic oscillator can be expanded in terms of Hermite functions. We find that this is possible for an infinite hierarchy of potentials discriminated by the parameter setting the strength of the centrifugal barrier. The $N$'th member of the hierarchy involves $N$ solutions for $N$ generally different values of the energy. For a particular member of the hierarchy, there exist infinitely many bound states with square integrable wave functions, written in terms of the Hermite functions, which vanish at the origin and at infinity. These bound states correspond to distinct values of the parameter setting the strength of the harmonic term. We also investigate connection with the polynomial solutions of the sextic oscillator obtained from the formalism of quasi-exactly solvable potentials.
