dorsal/arxiv
View SchemaInformation Entropy and Correlation of the Hooke's Atom
| Authors | Rajneesh Atre, Chandra Shekhar Mohapatra, Prasanta K. Panigrahi |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0411016 |
| URL | https://arxiv.org/abs/quant-ph/0411016 |
Abstract
We provide an algebraic procedure to find the eigenstates of two-charged particles in an oscillator potential, known as {\it{Hooke's}} atom. For the planar Hooke's atom, the exact eigenstates and single particle densities for arbitrary azimuthal quantum number, are obtained analytically. Information entropies associated with the wave functions for the relative motion are then studied systematically, since the same incorporates the effect of the Coulomb interaction. The {\it{quantum pottery}} of the information entropy density reveals a number of intricate structures, which differ significantly for the attractive and repulsive cases. We indicate the procedure to obtain the approximate eigen states. Making use of the relationship of this dynamical system with the quasi-exactly solvable systems, one can also develop a suitable perturbation theory, involving the Coulomb coupling $Z$, for the approximate wave functions.
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"abstract": "We provide an algebraic procedure to find the eigenstates of two-charged\nparticles in an oscillator potential, known as {\\it{Hooke\u0027s}} atom. For the\nplanar Hooke\u0027s atom, the exact eigenstates and single particle densities for\narbitrary azimuthal quantum number, are obtained analytically. Information\nentropies associated with the wave functions for the relative motion are then\nstudied systematically, since the same incorporates the effect of the Coulomb\ninteraction. The {\\it{quantum pottery}} of the information entropy density\nreveals a number of intricate structures, which differ significantly for the\nattractive and repulsive cases. We indicate the procedure to obtain the\napproximate eigen states. Making use of the relationship of this dynamical\nsystem with the quasi-exactly solvable systems, one can also develop a suitable\nperturbation theory, involving the Coulomb coupling $Z$, for the approximate\nwave functions.",
"arxiv_id": "quant-ph/0411016",
"authors": [
"Rajneesh Atre",
"Chandra Shekhar Mohapatra",
"Prasanta K. Panigrahi"
],
"categories": [
"quant-ph"
],
"title": "Information Entropy and Correlation of the Hooke\u0027s Atom",
"url": "https://arxiv.org/abs/quant-ph/0411016"
},
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