薛定谔方程中变形莫尔斯势的近似解析解

利用拉普拉斯变换和标度变换,求解了3维变形莫尔斯势条件下的薛定谔方程的近似解析解。通过将标度变换后的3维变形莫尔斯势作级数展开,忽略高阶微小量;合理选择相关参数,使得无解析解的情形转化为近似解析解存在。拉普拉斯变换中合理应用终值定理与卷积定理以及广义拉盖尔函数的正交性条件;获得了量子系统能谱的显式表示和归一化的本征波函数。

Approximate analytical solutions of Schrodinger for q-deformed Morse potential

Using Laplace integral transformation and the estimate transformation, the approximate analytical solutions of the 3 dimensional Schrodinger equation for q-deformed Morse potential is obtained. By means of expanding q-deformed Morse potential into the power series until the three order little term and smaller are ignored; sitting reasonably the parameter of wave function which is looked for makes the situation have essential change, so that the analytical solution without existence changes can turn into the approximate analytical solution existence; using reasonably terminal-value theorem and the convolution of Laplace integral transformation, and by applying the orthogonal condition of general Laguerre function, the explicit press of energy spectrum and the radial normalization eigenfunction of the quantum system are acquired.