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Physical Review A

Fisher information and semiclassical methods

Antonio Puente, M. Casas, Angel Ricardo Plastino

Published May 1, 1999• 4 citations
Publisher

Abstract

Using the Frieden and Soffer principle of extreme physical information we present a method for the construction of WKB wave functions that avoids the matching problem between the classically allowed and forbidden regions. When this formalism is applied in conjunction with the semiclassical methods for N-fermion systems, it provides one with Thomas-Fermi and Wigner-Kirkwood densities, valid beyond the turning points that also include shell effects. The method is illustrated with reference to both the sextic bistable and the Morse potential.

DOI
10.1103/physreva.59.3211

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Using the Frieden and Soffer principle of extreme physical information we present a method for the construction of WKB wave functions that avoids the matching problem between the classically allowed and forbidden regions. When this formalism is applied in conjunction with the semiclassical methods for N-fermion systems, it provides one with Thomas-Fermi and Wigner-Kirkwood densities, valid beyond the turning points that also include shell effects. The method is illustrated with reference to both the sextic bistable and the Morse potential.
A method is presented for the construction of WKB wave functions that avoids explicit consideration of any matching between results pertaining to classically allowed and classically forbidden regions. The formalism is based on the maximization of a suitably defined quantal pseudoentropy, subject to the constraints posed by the expectation values of a reduced number of operators, which are evaluated according to special WKB techniques that consider expansions up to orders \ensuremath{\Elzxh} and ${\mathrm{\ensuremath{\Elzxh}}}^{2}$. The algorithm is tested with reference to the harmonic and quartic anharmonic oscillators.
A method is presented for the construction of Wentzel-Kramers-Brillouin (WKB) wave functions that avoids explicit consideration of any matching between results pertaining to classically allowed and forbidden regions. The formalism is based on the maximization of a suitable defined quantal pseudoentropy, subject to the constraints posed by the expectation values of a reduced number of operators, which are evaluated according to special WKB techniques. A self-consistent procedure is developed that simultaneously yields the nodes of the wave function and the information theory parameters.
A long-standing problem and major shortcoming of semiclassical (WKB) bound-state wave functions is their divergence at the classical turning points. Presently available regularization schemes are accurate but rather complicated. It is shown how finite wave functions can be simply obtained by reorganizing the WKB perturbation expansion in powers of ℏ and retaining appropriate higher-order terms. The wave functions obtained by this method are compared with exactly known ones for the harmonic-oscillator and Morse potentials.