EXOTIC REPRESENTATIONS OF THE ISOTROPIC HARMONIC OSCILLATOR
1998 ◽
Vol 13
(19)
◽
pp. 3347-3360
Keyword(s):
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.
2002 ◽
Vol 35
(12)
◽
pp. 2979-2984
◽
2012 ◽
Vol 45
(46)
◽
pp. 465301
◽
2014 ◽
Vol 29
(21)
◽
pp. 1444015
Keyword(s):
1986 ◽
Vol 29
(2)
◽
pp. 211-219
◽
2018 ◽
Vol 118
(21)
◽
pp. e25727
◽
2019 ◽
Vol 17
(02)
◽
pp. 2050021
1997 ◽
Vol 12
(10)
◽
pp. 685-690
◽