Variational Principle Techniques and the Propertiesof a Cut-off and Anharmonic Wave Function

Abstract

The variational principles are very useful analytical tool for the study of the ground state energy of any dynamical system. In this work, we have evaluated the method and techniques of variational principle to derive the ground state energy for the harmonic, cut-off and anharmonic oscillators with a ground state wave function for a one-body Hamiltonian in three dimensions.

Analytical approximate bound state solution of Schrödinger equation in D -dimensions with a new mixed class of potential for arbitrary ℓ-state via asymptotic iteration method

“…These higher dimensional studies provide a general treatment of the problem in such a manner that one can obtain the required results in lower dimensions just dialing appropriate D. Many analytical as well as numerical techniques like the Laplace transform method [21][22][23], the Nikiforov-Uvarov method [24], the algebraic method [25], the 1 N expansion method [26], the path integral approach [27], the SUSYQM [28], the exact quantization rule [29] and others are applied to address Schrödinger equation both for lower and higher dimensional cases. In addition to that, hyperbolic potentials, exponential-type potentials or their combinations have attracted a lot of interest of different authors [30][31][32][33][34][35][36], both for multidimensional and lower dimensional Schrödinger equation. Bound state solutions of these potentials are very important in literature as they describe the different phenomenon like scattering, vibrational properties of molecules.…”

Closed Analytical Solutions of the D-Dimensional Schrödinger Equation with Deformed Woods–Saxon Potential Plus Double Ring-Shaped Potential

“…Many advanced mathematical methods have been used to solve it. Among the most popular methods, one can cite the variational method [1], the functional analysis method [2], the supersymetric method [3], the factorization method [4], the path integral method [5][6][7][8], the shifted 1/N expansion [9,10], the Nikiforov-Uvarov method (NU) [11,12] and the quantization rule approach [13,14]. Recently, the asymptotic iteration method (AIM) [15][16][17] an elegant, efficient technique to solve second-order homogeneous differential equations, has been the subject of extensive investigation in recent years, particularly when dealing withe non central potential.…”

Solution of Klein Gordon Equation for Some Diatomic Molecules with New Generalized Morse-like Potential Using SUSYQM

“…These techniques include asymptotic iteration method (AIM), 9 the Nikiforov-Uvarov method (NU), 10 supersymmetric quantum mechanices, 11 and others. Amongst the potentials studied with these techniques are the Manning-Rosen Potential, 12, 13 Hulthen Potential, 14,15 Eckarttype Potential, 16,17 Wood-Saxon Potential, 18,19 Poschl-Teller Potential. 20 Many contributions from different authors shows that the analytical solution of KGE are possible only in the swave case (l = 0) while for , it is solved by using suitable approximation scheme.…”