scholarly journals Gaussian decay for a difference of traces of the Schrödinger semigroup associated with the isotropic harmonic oscillator

2014 ◽  
Vol 419 (2) ◽  
pp. 1095-1118
Author(s):  
Mathieu Beau ◽  
Baptiste Savoie
Keyword(s):  
Harmonic Oscillator ◽  
Schrödinger Semigroup ◽  
Isotropic Harmonic Oscillator

scholarly journals Geometric Models of the Quantum Relativistic Rotating Oscillator

1997 ◽  
Vol 12 (10) ◽  
pp. 685-690 ◽  
Author(s):  
Ion I. Cotăescu
Keyword(s):  
Fine Structure ◽  
Harmonic Oscillator ◽  
Nonrelativistic Limit ◽  
Energy Spectra ◽  
De Sitter ◽  
Continuous Part ◽  
Geometric Models ◽  
Isotropic Harmonic Oscillator ◽  
Sitter Model ◽  
De Sitter Model

A family of geometric models of quantum relativistic rotating oscillator is defined by using a set of one-parameter deformations of the static (3+1) de Sitter or anti-de Sitter metrics. It is shown that all these models lead to the usual isotropic harmonic oscillator in the nonrelativistic limit, even though their relativistic behavior is different. As in the case of the (1+1) models,1 these will have even countable energy spectra or mixed ones, with a finite discrete sequence and a continuous part. In addition, all these spectra, except that of the pure anti-de Sitter model, will have a fine-structure, given by a rotator-like term.

scholarly journals Nodal Sets of Random Eigenfunctions for the Isotropic Harmonic Oscillator

2014 ◽  
Vol 2015 (13) ◽  
pp. 4813-4839 ◽  
Author(s):  
Boris Hanin ◽  
Steve Zelditch ◽  
Peng Zhou
Keyword(s):  
Harmonic Oscillator ◽  
Nodal Sets ◽  
Isotropic Harmonic Oscillator

EXOTIC REPRESENTATIONS OF THE ISOTROPIC HARMONIC OSCILLATOR

1998 ◽  
Vol 13 (19) ◽  
pp. 3347-3360
Author(s):  
LUIS J. BOYA ◽  
ERIC CHISOLM ◽  
S. M. MAHAJAN ◽  
E. C. G. SUDARSHAN
Keyword(s):  
Harmonic Oscillator ◽  
Rotation Group ◽  
Continuous Family ◽  
Ladder Operators ◽  
Standard Representation ◽  
Isotropic Harmonic Oscillator

We contruct and study a continuous family of representations of the N-dimensional isotropic harmonic oscillator (N≥2) which are not unitarily equivalent to the standard one. We explain why such representations exist and we investigate their simpler properties: the spectrum of the Hamiltonian (which contains nonstandard values), the form of the energy eigenfunctions, and their behavior under the ladder operators. Various symmetry and dynamical groups (e.g. the rotation group) which are valid on the standard representation are not implemented on the new ones. We comment very briefly on the prospects of observing these representations experimentally.

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