Solutions
of Schrodinger equation for a given
potential with any angular momentum have
much
attention
in chemical physics systems. Energy eigenvalues and the corresponding
eigenfunctions provide
a complete information about the diatomic molecules. Morse and Kratzer
potentials are one of the well-known diatomic potentials. The method used in
the Schrodinger equation for vibration-rotation states are mostly based on the
wave function expansion and exact solution for a single state with some
restrictions on the coupling constants. On the other hand
solutions of the
position-dependent effective-mass Schrodinger equation
are very interesting chemical
potential problem. They have also found important
applications in the fields of material science and condensed matter physics such
as semiconductors, quantum well and quantum dots, 3H, clusters, quantum
liquids, graded alloys and semiconductor heterostructures. Recently, number of
exact solutions on these topics increased. Various methods are used in the
calculations. The point canonical transformations (PCT) is one of these methods
providing exact solutions of energy eigenvalues and corresponding
eigenfunctions. It is also used for solving the Schrodinger equation with
position-dependent effective mass for some potentials.
In the present work, two different potentials solved with the
three mass distributions. The point canonical transformation is taken in the
more general form introducing a free parameter. This general form of the
transformation will provide us a set of solutions for different values of free parameter. In this work, the exact
solution of Schrodinger equation is obtained or the modified Kratzer type of
molecular potential and the corrected Morse potential. The contents of the paper
is as follows. In section 2, the solution of the Schrodinger presented briefly
by using point canonical transformation. In section 3, some applications for
the specific mass distributions introduced. Results are discussed in section 4.