Information entropy as a measure of tunneling and quantum confinement in a symmetric double-well potential

Abstract

Information entropic measures such as Fisher information, Shannon entropy, Onicescu energy and Onicescu Shannon entropy of a symmetric double-well potential are calculated in both position and momentum space. Eigenvalues and eigenvectors of this system are obtained through a variation-induced exact diagonalization procedure. The information entropy-based uncertainty relation is shown to be a better measure than conventional uncertainty product in interpreting purely quantum mechanical phenomena, such as, tunneling and quantum confinement in this case. Additionally, the phase-space description provides a semiclassical explanation for this feature. Total information entropy and phase-space area show similar behavior with increasing barrier height.

arXiv comment36 pages, 3 tables, 15 figures

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• Information-entropic measures for non-zero l states of confined hydrogen-like ions
• Exact and approximate solutions of Schrödinger's equation with hyperbolic double-well potentials
• Relative Fisher information in some central potentials
• Higher-order statistical correlations and mutual information among particles in a quantum well
• Information-Entropic Measures in Confined Isotropic Harmonic Oscillator
• Informational analysis of the confinement of an electron in an asymmetric double quantum dot