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Constructive inversion of energy trajectories in quantum mechanics

Richard L. Hall
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Abstract

We suppose that the ground-state eigenvalue E = F(v) of the Schroedinger Hamiltonian H = -Δ+ vf(x) in one dimension is known for all values of the coupling v > 0. The potential shape f(x) is assumed to be symmetric, bounded below, and monotone increasing for x > 0. A fast algorithm is devised which allows the potential shape f(x) to be reconstructed from the energy trajectory F(v). Three examples are discussed in detail: a shifted power-potential, the exponential potential, and the sech-squared potential are each reconstructed from their known exact energy trajectories.

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Richard L. Hall. 1998-12-18. Constructive inversion of energy trajectories in quantum mechanics. https://doi.org/10.1063/1.532712

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