Functional inversion for potentials in quantum mechanics

Details Functional inversion for potentials in quantum mechanics Functional inversion for potentials in quantum mechanics

1999-12-07

arxiv.org/abs/quant-ph/9912032v1

Phys. Lett. A265, 28-34 (2000)

Physics

Quantum Physics

14 pages, 2 figures

Scientific paper

10.1016/S0375-9601(99)00872-5

Let E = F(v) be the ground-state eigenvalue of the Schroedinger Hamiltonian H = -Delta + vf(x), where the potential shape f(x) is symmetric and monotone increasing for x > 0, and the coupling parameter v is positive. If the 'kinetic potential' bar{f}(s) associated with f(x) is defined by the transformation: bar{f}(s) = F'(v), s = F(v)-vF'(v),then f can be reconstructed from F by the sequence: f^{[n+1]} = bar{f} o bar{f}^{[n]^{-1}} o f^{[n]}. Convergence is proved for special classes of potential shape; for other test cases it is demonstrated numerically. The seed potential shape f^{[0]} need not be 'close' to the limit f.

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