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Relative Fisher information in some central potentials. (English) Zbl 1404.81064
Summary: Relative Fisher information (IR) was pursued for 1D quantum harmonic oscillator (QHO), 3D isotropic QHO, hydrogen atom and pseudoharmonic potential (PHP) in both \(r\) and \(p\) spaces. In 1D case, the \(n=0\) state is chosen as reference, whereas for a central potential, the respective circular (corresponding to lowest radial quantum number \(n_r\)) state of a given \(l\) quantum number, is selected. Starting from their exact wave functions, expressions of IR in both \(r\) and \(p\) spaces are obtained in closed analytical forms in all these systems. For the 1D QHO, IR in \(r, p\) spaces increases linearly with \(n\). For 3D QHO and PHP, it varies with single power of \(n_r\) in both spaces. But, in H atom they depend on both principal \((n)\) and azimuthal \((l)\) quantum numbers. However, at a fixed \(l\), IR initially advances with rise of \(n\) and then falls off; also for a given \(n\), it always decreases with \(l\).
MSC:
81P45 Quantum information, communication, networks (quantum-theoretic aspects)
94A17 Measures of information, entropy
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