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Exact R\'enyi entropies of $D$-dimensional harmonic systems
- Publication Year :
- 2018
-
Abstract
- The determination of the uncertainty measures of multidimensional quantum systems is a relevant issue \textit{per se} and because these measures, which are functionals of the single-particle probability density of the systems, describe numerous fundamental and experimentally accessible physical quantities. However, it is a formidable task (not yet solved, except possibly for the ground and a few lowest-lying energetic states) even for the small bunch of elementary quantum potentials which are used to approximate the mean-field potential of the physical systems. Recently, the dominant term of the Heisenberg and R\'enyi measures of the multidimensional harmonic system (i.e., a particle moving under the action of a $D$-dimensional quadratic potential, $D > 1$) has been analytically calculated in the high-energy (i.e., Rydberg) and the high-dimensional (i.e., pseudoclassical) limits. In this work we determine the exact values of the R\'enyi uncertainty measures of the $D$-dimensional harmonic system for all ground and excited quantum states directly in terms of $D$, the potential strength and the hyperquantum numbers.<br />Comment: Accepted in EPJ-ST
- Subjects :
- Physics
Physical system
General Physics and Astronomy
Probability density function
Harmonic (mathematics)
01 natural sciences
Action (physics)
010305 fluids & plasmas
symbols.namesake
Quantum state
0103 physical sciences
Rydberg formula
symbols
General Materials Science
Statistical physics
Physical and Theoretical Chemistry
010306 general physics
Quantum
Mathematical Physics
Physical quantity
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....16150e866898f9614487490efa81fdad