Untitled

On solutions of the Schrödinger equation for some molecular potentials: wave function ansatz

“…Hence if it is exactly solvable for a given potential, the wave function can describe such a system completely. Until now, many efforts have been made to solve the stationary SE with anharmonic potentials in three dimensions and two dimensions [1][2][3][4][5][6] with many applications to molecular and chemical physics. The study of the SE with these potentials provides us with insight into the physical problem under consideration.…”

Exact solutions of the D-dimensional Schrödinger equation for a ring-shaped pseudoharmonic potential

“…In principle, since π( ) has to be a polynomial of degree at most one, the expression under the square root sign in (10) can be arranged to be the square of a polynomial of first degree [66]. This is possible only if its discriminant is zero.…”

“…In this case, an equation for is obtained. After solving this equation, the obtained values of are substituted in (10). In addition, by comparing Eqs.…”

“…(43) Inserting the above expressions into equation (10) and taking σ ( ) = −2 , one obtains the following function:…”

“…Hence approximation methods are used to obtain their solutions [1][2][3][4]. So far, much work in this direction has been done for solving the stationary SE with anharmonic potentials in two dimensions (2D) and three dimensions (3D) [5][6][7][8][9][10] with many applications to molecular and chemical physics. The study of the SE with these potentials provides us with insight into the physical problem under consideration.…”