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Functional inversion for potentials in quantum mechanics

Authors
Journal
Physics Letters A
0375-9601
Publisher
Elsevier
Publication Date
Volume
265
Identifiers
DOI: 10.1016/s0375-9601(99)00872-5

Abstract

Abstract Let E= F( v) be the ground-state eigenvalue of the Schrödinger Hamiltonian H=− Δ+ 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 f ̄ (s) associated with f( x) is defined by the transformation f ̄ (s)=F′(v), s=F(v)−vF′(v) , then f can be reconstructed from F by the sequence f [n+1]= f ̄ ∘ f ̄ [n] −1 ∘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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