论文标题
与位置依赖性质量施罗丁方程的精确溶液具有完全正振荡器形的量子孔电位
Exact solution of the position-dependent mass Schrödinger equation with the completely positive oscillator-shaped quantum well potential
论文作者
论文摘要
提出了两个完全阳性振荡器形量子井的确切可溶解的密闭模型。提出了与所提出的量子井电位相对应的位置依赖性群schrödinger方程的精确溶液。结果表明，两个模型的离散能谱表达式取决于某些正限制参数。频谱对模型表现出正等距行为，仅限制了一个无限高的壁和非轨道行为的模型，而该模型与两侧无限高壁的模型相比。通过Laguerre和Jacobi多项式表达了正在构建模型的固定状态的波形。通常，在波函数中出现的雅各比多项式取决于参数$ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $。讨论了构造模型的一些限制和特殊情况。
Two exactly-solvable confined models of the completely positive oscillator-shaped quantum well are proposed. Exact solutions of the position-dependent mass Schrödinger equation corresponding to the proposed quantum well potentials are presented. It is shown that the discrete energy spectrum expressions of both models depend on certain positive confinement parameters. The spectrum exhibits positive equidistant behavior for the model confined only with one infinitely high wall and non-equidistant behavior for the model confined with the infinitely high wall from both sides. Wavefunctions of the stationary states of the models under construction are expressed through the Laguerre and Jacobi polynomials. In general, the Jacobi polynomials appearing in wavefunctions depend on parameters $a$ and $b$, but the Laguerre polynomials depend only on the parameter $a$. Some limits and special cases of the constructed models are discussed.
