Bound state solution of the Schrödinger equation for Mie potential

Abstract

Exact solution of Schrödinger equation for the Mie potential is obtained for an arbitrary angular momentum. The energy eigenvalues and the corresponding wavefunctions are calculated by the use of the Nikiforov-Uvarov method. Wavefunctions are expressed in terms of Jacobi polynomials. The bound states are calculated numerically for some values of ℓ and n with n ≤ 5. They are applied to several diatomic molecules.

Exact solutions of the Schrödinger equation for the pseudoharmonic potential: an application to some diatomic molecules

“…Several other potentials are been used as alternatives and their performances have been compared with the Morse potential [43,[46][47][48][49][50][51][52][53][54][55][56]. For examples, Kratzer and pseudoharmonic potentials which have known exact solutions like in the Coulomb and harmonic oscillator model potentials [31,45,[57][58][59][60][61].…”

“…Its characteristics make it useful to model various physical systems, including some molecular physical ones [9,31,59,68,69,72]. From the mathematical point of view, it resembles the harmonic oscillator, from which it deviates by two correction terms depending on the potential depth and the equilibrium distance parameter r e : the first one is an energy shift and the second one is a modified centrifugal term.…”

“…In the study of the diatomic molecules using the diatomic molecular potentials, different methods have been employed: Nikiforov-Uvarov method [42][43][44][45][57][58][59]; asymptotic iteration method [60]; Exact method [72]; shifted 1/N expansion [40]; exact quantization rule method [46,61]; SUSY approach [41]; Nikiforov-Uvarov method [45,57,59]; tridiagonal J-matrix representation [75,76] and algebraic method [31,77].…”

An alternative solution of diatomic molecules

“…The Pseudoharmonic potential is one of the exactly solvable potentials and defines the real physical systems that have generally anharmonical properties [57]. It can be written as [58] …”

A General Approach for the Exact Solution of the Schrödinger Equation

“…These potentials are Morse [41], Rosen-Morse [42][43][44], Pseudoharmonic [45,46], Mie [47][48][49][50][51][52][53][54], Woods-Saxon [55][56][57][58][59][60][61], Poschl-Teller [62][63][64][65][66], Kratzer-Fues [67,68], Noncentral [69][70][71][72]. Woods-Saxon potential describes the interaction of a neutron with a heavy nucleus.…”