Wigner function for a particle in delta-potential and in a box

Saul T. Epstein

E. P. Wigner has shown that although there are reasons why one might hope to succeed, one cannot in fact derive the binding energy of the hydrogen atom by second-order perturbation theory applied to a free particle in a box. To further clarify the reasons for this failure we here consider the one-dimensional attractive delta function potential.

E. Cancellieri, Paolo Bordone, Andrea Bertoni +2 more

Hai-Woong Lee

Pouria Pedram, Mohammad Vahabi

We use the factorization method to find the exact eigenvalues and eigenfunctions for a particle in a box with the delta function potential V(x)=λδ(x−x0). We show that the presence of the potential results in the discontinuity of the corresponding ladder operators. The presence of the delta function potential allows us to obtain the full spectrum in the first step of the factorization procedure even in the weak coupling limit λ→0.

Bruce L. Scott

The problem of a particle interacting with a potential of delta-function shape and having a tensor component is considered for box boundary conditions. The limits of small potential and large box dimensions are considered, especially in their effect on the mixing parameter.

Antoine Royer