Exact solutions to solitonic profile mass Schrödinger problem with a modified Pöschl-Teller potential

We present exact solutions of solitonic profile mass Schrödinger equation with a modified Pöschl-Teller potential. We find that the solutions can be expressed analytically in terms of confluent Heun functions. However, the energy levels are not analytically obtainable except via numerical calculations. The properties of the wave functions, which depend on the values of potential parameter - are illustrated graphically. We find that the potential changes from single well to a double well when parameter - changes from minus to positive. Initially, the crest of wave function for the ground state diminishes gradually with increasing - and then becomes negative. We notice that the parities of the wave functions for n > 1 also change.