CAJ | 학술논문

在球坐标系中研究了一类具有运动边界与含时频率的环状非球谐振子模型势的Schrdinger方程.应用坐标变换将运动边界转化为固定边界, 从而获得了系统的精确波函数. 研究表明, 系统的角向波函数是一个推广的缔合勒让德多项式, 径向波函数可以表示为贝赛耳函数.最后我们简单讨论了指数运动边界和指数含时频率这一特殊情况.
재구좌표계중연구료일류구유운동변계여함시빈솔적배상비구해진자모형세적Schrdinger방정.응용좌표변환장운동변계전화위고정변계, 종이획득료계통적정학파함수. 연구표명, 계통적각향파함수시일개추엄적체합륵양덕다항식, 경향파함수가이표시위패새이함수.최후아문간단토론료지수운동변계화지수함시빈솔저일특수정황.
Using the coordinate transformation transforming the moving boundary conditions to the fixed boundary conditions, we study the exact solution to the Schr(o)dinger equation for a kind of ring-shaped non-harmonic oscillator model potential with moving boundaries and time-dependent frequency in the spherical coordinates. The general associated-Legendre-type angular wave function and the Bessel-type radial wave function are obtained. The special case for exponential-type boundaries and corresponding time-dependent frequency is also studied breifly.