一维有限深方势阱中的束缚态

主要对量子力学一维有限深方势阱中运动粒子的束缚态存在条件进行讨论.通过求解定态薛定谔方程,得到粒子运动满足的超越方程,借助于Mathematica软件求解该超越方程得到粒子的能级结构,对粒子束缚态存在条件进行分析.结果表明,对于在一维有限深对称方势阱中运动的粒子,总会有束缚态的存在,和势阱的宽度、深度及粒子的质量无关.而在半壁有限深势阱中运动的粒子,出现束缚态是有条件的.并且分别给出了在两种势阱中粒子存在多个束缚态需要满足的条件.

Bound States in One Dimensional Square Well with Finite Depth

In the paper,we mainly discuss the existence conditions of bound state for a particle moving in one-dimension finite square well and the uncertainty principle.A transcendental equation for the energy of the particle is obtained by solving the Schrodinger equation.The equation is solved and the energy levels are obtained with the help of software Mathematica.Besides,we analyze the existence of the bound states.Our results show that there is always one bound state for the particle in one-dimension symmetric finite square well,no matter how shallow or narrow the well becomes and no matter what the mass of the particle is.Whereas there exists condition for a particle moving in a half finite square well.What′s more,we give the conditions for the existence of numbers of the bound states in these two square well,respectively.