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Information entropy as a measure of tunneling and quantum confinement in a symmetric double-well potential. (English) Zbl 1337.81047
Summary: 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 semi-classical explanation for this feature. Total information entropy and phase-space area show similar behavior with increasing barrier height.

MSC:
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
94A17 Measures of information, entropy
49S05 Variational principles of physics (should also be assigned at least one other classification number in Section 49-XX)
81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
81S30 Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics
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