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Register a new userVirial ansatze for the Schrodinger Equation with a symmetric strictly convex potential. Part II
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Added by
Silvana Pilar Flego
Publication date
2021
fields
Physics
and research's language is
English
Authors
S. P. Flego
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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.
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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 still be verified, parameter-free ansatze for the eigenfunctions of the associated Schrodinger equation are built. To illustrate the process, the technique is successfully tested against the harmonic oscillator, in which it leads to the exact eigenfunctions, and against the quartic anharmonic oscillator, which is considered the paradigmatic testing ground for new approaches to the Schrodinger equation.
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