Quantum-information entropies for highly excited states of single-particle systems with power-type potentials
- Instituto Carlos I de Fisica Teorica y Computacional, Granada University, Granada (Spain)
The asymptotics of the Boltzmann-Shannon information entropy as well as the Renyi entropy for the quantum probability density of a single-particle system with a confining (i.e., bounded below) power-type potential V(x)=x{sup 2k} with k is a member of N and x is a member of R, is investigated in the position and momentum spaces within the semiclassical (WKB) approximation. It is found that for highly excited states both physical entropies, as well as their sum, have a logarithmic dependence on its quantum number not only when k=1 (harmonic oscillator), but also for any fixed k. As a by-product, the extremal case k{yields}{infinity} (the infinite well potential) is also rigorously analyzed. It is shown that not only the position-space entropy has the same constant value for all quantum states, which is a known result, but also that the momentum-space entropy is constant for highly excited states.
- OSTI ID:
- 20632404
- Journal Information:
- Physical Review. A, Vol. 66, Issue 6; Other Information: DOI: 10.1103/PhysRevA.66.062109; (c) 2002 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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