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Spectral Properties of Confining Superexponential Potentials

by Peter Schmelcher

Submission summary

As Contributors: Peter Schmelcher
Preprint link: scipost_202103_00018v1
Date submitted: 2021-03-17 18:20
Submitted by: Schmelcher, Peter
Submitted to: SciPost Physics
Academic field: Physics
  • Quantum Physics
Approach: Theoretical


We explore the spectral properties and behaviour of confining superexponential potentials. Several prototypes of these highly nonlinear potentials are analyzed in terms of the eigenvalues and eigenstates of the underlying stationary Schrödinger equation up to several hundreds of excited states. A generalization of the superexponential self-interacting oscillator shows a scaling behaviour of the spacing of the eigenvalues which turns into an alternating behaviour for the power law modified oscillator. Superexponential potentials with an oscillating power show a very rich spectral structure with varying amplitudes and wave vectors. In the parity symmetric case doublets of near degenerate energy eigenvalues emerge in the spectrum. The corresponding eigenstates are strongly localized in the outer wells of the potential and occur as even-odd pairs which are interspersed into the spectrum of delocalized states. We provide an outlook on future perspectives including the possibility to use these features for applications in e.g. cold atom physics.

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Submission scipost_202103_00018v1 on 17 March 2021

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