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Some complexity measures in confined isotropic harmonic oscillator. (English) Zbl 1433.82004
Summary: Various well-known statistical measures like López-Ruiz, Mancini, Calbet (LMC) and Fisher-Shannon complexity have been explored for confined isotropic harmonic oscillator (CHO) in composite position (\(r\)) and momentum (\(p\)) spaces. To get a deeper insight about CHO, a more generalized form of these quantities with Rényi entropy (\(R\)) is invoked here. The importance of scaling parameter in the exponential part is also investigated. \(R\) is estimated considering order of entropic moments \(\alpha , \beta \) as \((\frac{2}{3},3)\) in \(r\) and \(p\) spaces respectively. Explicit results of these measures with respect to variation of confinement radius \(r_c\) is provided systematically for first eight energy states, namely, \(1s\), \(1p\), \(1d\), \(2s\), \(1f\), \(2p\), \(1g\) and \(2d\). This investigation advocates that (i) CHO may be treated as a missing-link between PISB and IHO (ii) an increase in number of nodes takes the system towards order. A detailed analysis of these complexity measures reveals several other hitherto unreported interesting features.
MSC:
82B10 Quantum equilibrium statistical mechanics (general)
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