Arbitrarily Accurate Eigenvalues for General Anharmonic Potentials

Details Arbitrarily Accurate Eigenvalues for General Anharmonic Potentials Arbitrarily Accurate Eigenvalues for General Anharmonic Potentials

2002-02-07

arxiv.org/abs/quant-ph/0202047v3

J.Phys.A35:8831-8846,2002

Physics

Quantum Physics

10 pages, 8 figures, uses revtex; new section added, references added

Scientific paper

10.1088/0305-4470/35/41/314

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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