Exact Solutions of the Morse-like Potential,Step-Up and Step-Down Operators via Laplace Transform Approach

Sedigheh Miraboutalebi, Leila Rajaei

Altuğ Arda, Ramazan Sever

M. Zarezadeh, Mohammad Kazem Tavassoly

In this paper, we have solved the Schrödinger equation for a particular kind of Morse potential and find its normalized eigenfunctions and eigenvalues, exactly. Our work is based on the Laplace transform technique which reduces the second-order differential equation to a first-order.

Tapas Das, Altuğ Arda

The second-order N -dimensional Schrödinger equation with pseudoharmonic potential is reduced to a first-order differential equation by using the Laplace transform approach and exact bound state solutions are obtained using convolution theorem. Some special cases are verified and variations of energy eigenvalues En as a function of dimension N are furnished. To give an extra depth of this paper, the present approach is also briefly investigated for generalized Morse potential as an example.

Shi‐Hai Dong, Guo-Hua Sun

Sedigheh Miraboutalebi

In the framework of the position-dependent mass quantum mechanics, the three dimensional Schrödinger equation is studied by applying the Laplace transforms combining with the point canonical transforms. For the potential analogues to Morse potential and via the Pekeris approximation, we introduce the general solutions appropriate for any kind of position dependent mass profile which obeys a key condition. For a specific position-dependent mass profile, the bound state solutions are obtained through an analytical form. The constant mass solutions are also relived.