Functional Inversion for Potentials in Quantum Mechanics


Let E = F (v) be the ground-state eigenvalue of the Schrödinger Hamiltonian H = −∆ + 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 f̄(s) associated with f(x) is defined by the transformation f̄(s) = F ′(v), s = F (v) − vF ′(v), then f can be… (More)


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