Quantum-information entropies for highly excited states of single-particle systems with power-type potentials
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^2k with k∈N and x∈R, is investigated in the position and momentum spaces within...
| Main Authors: | , , |
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| Format: | info:eu-repo/semantics/article |
| Language: | English |
| Published: |
American Physical Society
2017
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| Online Access: | http://hdl.handle.net/10835/4869 https://doi.org/10.1103/PhysRevA.66.062109 |
| Summary: | 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^2k with k∈N and x∈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→∞ (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. |
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