Bound states of one-dimensional potential

Chandan Kumar

Zhan Wei Xu

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.

J. D. Kelley, Jacob J. Leventhal

Le Wang

For a moving particle in an semi- infinite potential well of one dimension,a continuous and monotonous function is introduced by solving stationary Schr? dinger equation,then Existence conditions of one even more Particle's bound state are analyzed by means of the zero- point theorem of continuous function. The results show the number of bound state is connected with the width and depth of one – dimensional Infinite potential well. For a certain quality of particle,more bound states need much deeper and wider potential well.

Rocco Schiavilla

Bound states in one-dimensional finite and infinite wells and delta-function potentials, and combinations of these, are obtained; the WKB method for bound states is introduced; the consequences of a parity-invariant potential for the eigenfunctions are derived.

S. Brandt, Hans Dieter Dahmen, Tilo Stroh