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Arbitrarily Accurate Eigenvalues for General Anharmonic Potentials

Y. Meurice
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Abstract

We show that the Riccati form of the Schrodinger equation can be reformulated in terms of two linear equations depending on an arbitrary function G. When $G$ and the potential are polynomials, the solutions of these two equations are entire functions (L and K) and the zeroes of K are identical to those of the wave function. Requiring such a zero at a large but finite value of the argument yields the low energy eigenstates with exponentially small errors. Judicious choice of G can improve dramatically the numerical treatment. The method yields many significant digits with modest computer means.

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Y. Meurice. 2002-09-06. Arbitrarily Accurate Eigenvalues for General Anharmonic Potentials. https://doi.org/10.1088/0305-4470%2F35%2F41%2F314

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