超对称算符方法求解一维束缚态的应用

New application of supersymmetric operator method to one dimensional bound states

由量子力学算符的因式分解出发，结合超势的形状不变性，运用超对称算符方法严格求解了一维势阱Ｓｃａｒｆ（Ⅱ）势的束缚态能级和波函数，并讨论了其束缚态的存在性。考察了形状类似的一维方势阱—势垒，发现只在一定条件下才存在束缚态。类比其它各种形状的方势阱和连续变化势阱，对一维束缚态的存在条件作了较普遍的讨论，发现它与一维势的形状密切相关。

Starting from the operator factorization in Quantum Mechanics and combined with the shape invariance of superpotential, the supersymmetric operator method can be used to exactly solve the energies and wavefunctions of bound states in a one dimensional potential well, Scarf(Ⅱ) potential. And the existence of its bound states was discussed. The similar one dimensional square well barrier was also investigated and conditions for existence of bound states were also found. Comparing other various square potential wells with continuous ones, the general discussion for existence condition of one dimensional bound states was given and it is found that this existence condition is closely related with the shapes of one dimensional potentials.