函数. 本文基于超越方程的泰勒级数展开，给出了一级近似下能谱及其波函数的解析解，发现束缚态个数由一个无量纲参数R

确定，该参数正比于势阱宽度乘以势阱高度开方. 除了最高能级波函数，能谱及其波函数的近似解析解与数值结果吻合. 大R

极限下，发现近似解析解退化为可精确求解的无限深势阱情况.

energy spectrum and its wave function can be obtained from a transcendental equation. In this paper，we solve the

transcendental equation with the Taylor series expansion，which to the first order gives analytical solutions of the energy

spectrum and its wave function. We find that the number of bound states is determined by a dimensionless parameter

R，which is proportional to the width of the well multiplied by the square of the potential height. Except the highest

level wave function，the approximate analytical results show in well agreement with the numerical results. In the

limit of large R，the approximate analytical results recover the exactly solvable problem of an infinite square well.