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Open Quantum Systems Decoherence

Supersymmetric partner potentials arising from nodeless half bound states

arXiv

Authors: Zafar Ahmed, Dhruv Sharma, Rahul Kaiwart, Mohammad Irfan

Year

2016

Paper ID

41686

Status

Preprint

Abstract Read

~2 min

Abstract Words

163

Citations

N/A

Abstract

A Half Bound State (HBS) ψ_*(x) can be defined as a single, conditional, zero-energy, continuous solution of the one dimensional Schr{ö}dinger equation for a scattering potential well V(x) $s.t V(pm infty=0). The non-normalizable and solitary HBS of a potential satisfies Neumann boundary condition thatψ'_*pm infty=0and it can haven$= 0,1,2,...$ number of nodes indicatingnnumber of bound states inV(x)belowE=0. Here we show that starting with a nodeless HBS, we can construct a (supersymmetric) pair of finite potentials (well, double wells, well-barrier):V_{\pm}(x)having no bound state and they enclose positive area onx-axis. On the contrary their negative counterparts-cV_pm(x),c>0do have at least one bound state for any arbitrary positive value ofc. Furthermore,c V_{\pm}(x), c >0which binds positive area on x-axis in conformity with Simon's theorem can have at least one bound state only conditionally for instance whenc>1orc>>1$.

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A Half Bound State (HBS) ψ_*(x) can be defined as a single, conditional, zero-energy, continuous solution of the one dimensional Schrödinger equation for a scattering potential...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1612.07081 [2] arXiv https://arxiv.org/abs/1612.07081 [3] Publisher https://arxiv.org/abs/1612.07081

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