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Recently was introduced in the literature a procedure to obtain ansatze, free of parameters, for the eigenfunctions of the time-independent Schrodinger equation with symmetric convex potential. In the present work, we test this technique in regard to $x^{2kappa}$-type potentials. We study the behavior of the ansatze regarding the degree of the potential and to the intervening coupling constant. Finally, we discuss how the results could be used to establish the upper bounds of the relative errors in situations where intervening polynomial potentials.
Considering symmetric strictly convex potentials, a local relationship is inferred from the virial theorem, based on which a real log-concave function can be constructed. Using this as a weight function and in such a way that the virial theorem can s
In this paper, we search the dependence of some statistical quantities such as the free energy, the mean energy, the entropy, and the specific heat for the Schrodinger equation on the temperature, particularly the case of a non-central potential. The
A general form of the effective mass Schrodinger equation is solved exactly for Hulthen potential. Nikiforov-Uvarov method is used to obtain energy eigenvalues and the corresponding wave functions. A free parameter is used in the transformation of the wave function.
In this paper, we show the scattering of the solution for the focusing inhomogenous nonlinear Schrodinger equation with a potential begin{align*} ipartial_t u+Delta u- Vu=-|x|^{-b}|u|^{p-1}u end{align*} in the energy space $H^1(mathbb R^3)$. We pro
The scattering solutions of the one-dimensional Schrodinger equation for the Woods-Saxon potential are obtained within the position-dependent mass formalism. The wave functions, transmission and reflection coefficients are calculated in terms of Heun