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Open Quantum Systems Decoherence Quantum Simulation

Confining non-analytic exponential potential V(x)= g2exp (2|x|) and its exact Bessel-function solvability

arXiv
Authors: Ryu Sasaki

Year

2016

Paper ID

42512

Status

Preprint

Abstract Read

~2 min

Abstract Words

131

Citations

N/A

Abstract

In a previous paper we have shown that Schrödinger equation with the non-analytic attractive exponential potential V(x)= -g2exp (-|x|) is exactly solvable. It has finitely many discrete eigenstates described by the Bessel function of the first kind J_ν(z) and the eigenvalues are specified by the positive zeros of J_ν(g) and J'_ν(g) as a function of the order ν with fixed g>0. Now we show the corresponding results for the {\em confining\/} non-analytic exponential potential V(x)= g2exp (2|x|). This has infinitely many discrete eigenstates described by the modified Bessel function of the second kind Kiν(z). The eigenvalues are specified by the {\em pure imaginary zeros\/} of Kiν(g) and K'iν(g) as a function of the order with fixed g>0.

Why This Paper Matters

  • This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
  • It adds a 2016 reference point for readers tracking recent quantum research.
  • In a previous paper we have shown that Schrödinger equation with the non-analytic attractive exponential potential V(x)= -g^2exp (-|x|) is exactly solvable.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1611.02467 [2] arXiv https://arxiv.org/abs/1611.02467 [3] Publisher https://arxiv.org/abs/1611.02467

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