Quantum confinement in an asymmetric double-well potential through energy analysis and information entropic measure. (arXiv:1904.06076v1 [quant-ph])

Localization of a particle in the wells of an asymmetric double-well (DW)
potential is investigated here. Information entropy-based uncertainty measures,
such as Shannon entropy, Fisher information, Onicescu energy, etc., and
phasespace area, are utilized to explain the contrasting effect of
localization-delocalization and role of asymmetric term in such two-well
potentials. In asymmetric situation, two wells behaves like two different
potentials. A general rule has been proposed for arrangement of
quasi-degenerate pairs, in terms of asymmetry parameter. Further, it enables to
describe the distribution of particle in either of the deeper or shallow wells
in various energy states. One finds that, all states eventually get localized
to the deeper well, provided the asymmetry parameter attains certain threshold
value. This generalization produces symmetric DW as a natural consequence of
asymmetric DW. Eigenfunctions, eigenvalues are obtained by means of a simple,
accurate variationinduced exact diagonalization method. In brief, information
measures and phase-space analysis can provide valuable insight toward the
understanding of such potentials.

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