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The quantum harmonic oscillator on the sphere and the hyperbolic plane: -dependent formalism, polar coordinates, and hypergeometric functions
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10.1063/1.2795214
/content/aip/journal/jmp/48/10/10.1063/1.2795214
http://aip.metastore.ingenta.com/content/aip/journal/jmp/48/10/10.1063/1.2795214
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Plot of the central potential , as a function of , for and for (hyperbolic case, lower curves), (dash line), and (spherical case, upper curves).

Image of FIG. 2.
FIG. 2.

Plot of three radial functions with quantum numbers , : the Euclidean function (, dashed curve) and two -dependent functions corresponding to and . For very small values of the curvature the figure is very close to the radial curve but when the value of increases the oscillations narrow and move into smaller values of .

Image of FIG. 3.
FIG. 3.

Plot of three radial functions with quantum numbers , : the Euclidean function (, dashed curve) and two -dependent functions corresponding to and . When the absolute value increases then the oscillations soften and lengthen into greater values of .

Image of FIG. 4.
FIG. 4.

Plot of the energy as a function of , , for several values of the curvature with the thick points representing the energies of the bound states. The upper curves correspond to two spherical cases, and ; the straight line parallel to the diagonal (dashed line) represents the standard Euclidean case and the lower curves represent two hyperbolical cases (four bound levels) and (only two bound levels).

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/content/aip/journal/jmp/48/10/10.1063/1.2795214
2007-10-16
2014-04-23
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: The quantum harmonic oscillator on the sphere and the hyperbolic plane: κ-dependent formalism, polar coordinates, and hypergeometric functions
http://aip.metastore.ingenta.com/content/aip/journal/jmp/48/10/10.1063/1.2795214
10.1063/1.2795214
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