Multi-point quasi-rational approximants for the energy eigenvalues of potentials of the form V(x)= Ax^a + Bx^b

P. Martin; A. De Freitas; E. Castro; J. L. Paz

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arXiv · 0810.2334

Multi-point quasi-rational approximants for the energy eigenvalues of potentials of the form V(x)= Ax^a + Bx^b

P. Martin·A. De Freitas·E. Castro·J. L. Paz

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Abstract

Analytic approximants for the eigenvalues of the one-dimensional Schrödinger equation with potentials of the form $V(x)= Ax^a + Bx^b$ are found using a multi-point quasi-rational approximation technique. This technique is based on the use of the power series and asymptotic expansion of the eigenvalues in $λ=A^{-\frac{b+2}{a+2}}B$, as well as the expansion at intermediate points. These expansions are found through a system of differential equations. The approximants found are valid and accurate for any value of $λ$. As examples, the technique is applied to the quartic and sextic anharmonic oscillators.

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P. Martin, A. De Freitas, E. Castro, J. L. Paz. 2008-10-13. Multi-point quasi-rational approximants for the energy eigenvalues of potentials of the form V(x)= Ax^a + Bx^b. https://arxiv.org/abs/0810.2334

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