Exact solution of the Schrödinger equation with a new expansion of anharmonic potential with the use of the supersymmetric quantum mechanics and factorization method

Abstract

The study involves finding exact eigenvalues of the radial Schrödinger equation for new expansion of the anharmonic potential energy function. All analytical calculations employ the mathematical formalism of the supersymmetric quantum mechanics. The novelty of this study is underlined by the fact that for the first time the recurrence formulas for rovibrational bound energy levels have been derived employing factorization method and algebraic approach. The ground state and the excited states have been determined by means of the hierarchy of the isospectral Hamiltonians. The Riccati nonlinear differential equation with superpotentials has been solved analytically. It has been shown that exact solutions exist when the potential and superpotential parameters satisfy certain supersymmetric constraints. The results obtained can be utilized both in computations of quantum chemistry and theoretical spectroscopy of diatomic molecules.

Computation of energy eigenvalues of the anharmonic Coulombic potential with irregular singularities

“…In [35], exact eigenvalues were found form the radial Schrödinger equation for the anharmonic potential given by:…”

Effects of Two-Dimensional Noncommutative Theories on Bound States Schrödinger Diatomic Molecules under New Modified Kratzer-Type Interactions

“…[1][2][3]. In particular, the modified Kratzer-type potential (MKP) have the general features of the true interaction energy, inter atomic and dynamical properties in solid-state physics and play an important role in the history of molecular structures molecular physics ( 2 N , CO , NO , CH ,… ) and interactions [4][5][6], in addition, this potential offered one of the most important exactly models of atomic and molecular physics and quantum chemistry.…”

Operadores-escada generalizados para sistemas quânticos

“…Em comparaçãoà resolução direta da equação de Schrödinger independente do tempo, este formalismo permite, por exemplo, uma simplificação dos cálculos e atacar outros tipos de problemas, como aqueles envolvendo potenciais parcialmente solúveis [3][4][5][6]. Assim, essa abordagem tem motivado muitos estudos e estendido a compreensão sobre diversos sistemas quânticos (vide, por exemplo, 11] e usando a chamada Shape Invariance do potencial [1,2,9,10,[12][13][14][15][16].…”

“…Assim, essa abordagem tem motivado muitos estudos e estendido a compreensão sobre diversos sistemas quânticos (vide, por exemplo, Ref. [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]). …”

“…Em especial, eleéútil para estudar potenciais exatamente solúveis [1][2][3][7][8][9][10][11][12][13][14][15][16] e parcialmente solúveis [1][2][3][4][5][6]18]. Em potenciais exatamente solúveis, o formalismo oferece duas vias de solução: através da Hierarquia de Hamiltonianos [1][2][3]7, * Endereço de correspondência: josimarfsilva@sjrp.unesp.br.…”