Exact Solution of Schrödinger Equation with Inverted Woods-Saxon and Manning-Rosen Potentials

Abstract

We have analytically solved the radial Schrödinger equation with inverted Woods-Saxon and Manning-Rosen Potentials. With the ansatz for the wave function, we obtain the generalized wave function and the negative energy spectrum for the system.

Bound state solutions of the Schrödinger equation with energy-dependent molecular Kratzer potential via asymptotic iteration method

“…The solution of this equation is used in the description of particle dynamics in the non-relativistic regime 3,4 . Even though the Schrödinger equation was developed many decades ago, it is still very challenging to solve it analytically 5,6 . The solution of the Schrödinger equation contains all the necessary information needed for the full description of a quantum state such as the probability density and entropy of the system 7,8 .…”

Nonrelativisitic Treatment of Schrodinger Particles under Inversely Quadratic Hellmann Plus Ring-Shaped Potential

“…The exact bound-state solutions of the Schrödinger equation with physically significant potentials play a major role in quantum mechanics [1][2][3][4][5]. Interestingly, one of the important tasks in theoretical physics is to obtain the exact solution of the Schrödinger equation for special potentials [6][7][8][9][10]. Some of these potentials are known to play important roles in many fields of physics such as molecular, solid-state, and chemical physics [11][12][13].…”

Solitary Wave Solutions of Some Coupled Nonlinear Evolution Equations

“…However, not all equations posed of these models are solvable. As a result, many new techniques have been successfully developed by diverse groups of mathematicians and physicists, such as the Hirota's bilinear transformation method [1,2], the tanh-function method [3,4], the extended tanh-method [5,6], the Exp-function method [7][8][9][10][11], the Adomian decomposition method [12], the F-expansion method [13], the auxiliary equation method [14], the Jacobi elliptic function method [15], the modified exp-function method [16], the (G'/G)-expansion method [17][18][19][20][21][22][23][24][25][26], the Weierstrass elliptic function method [27], the homotopy perturbation method [28][29][30], the homogeneous balance method [31,32], the modified simple equation method [33][34][35][36], the enhanced (G'/G)-expansion method [37], the exp(-Φ(ξ))-expansion method [38], the ansatz method [39], the functional variable method [40] and so on.…”