Non-linear ladder operators and coherent states for the 2:1 oscillator
- URL: http://arxiv.org/abs/2011.10145v2
- Date: Tue, 22 Jun 2021 20:06:57 GMT
- Title: Non-linear ladder operators and coherent states for the 2:1 oscillator
- Authors: James Moran, V\'eronique Hussin, Ian Marquette
- Abstract summary: The 2:1 two-dimensional anisotropic quantum harmonic oscillator is considered and new sets of states are defined.
The states generated are good candidates for the natural generalisation of the $mathfraksu(2)$ coherent states.
The uncertainty relations of the defining chain of states are calculated and it is found that they admit a resolution of the identity and the spatial distribution of the wavefunction produces Lissajous figures.
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- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The 2:1 two-dimensional anisotropic quantum harmonic oscillator is considered
and new sets of states are defined by means of normal-ordering non-linear
operators through the use of non-commutative binomial theorems as well as
solving recurrence relations. The states generated are good candidates for the
natural generalisation of the $\mathfrak{su}(2)$ coherent states of the
two-dimensional isotropic oscillator. The two-dimensional non-linear
generalised ladder operators lead to several chains of states which are
connected in a non trivial way. The uncertainty relations of the defining chain
of states are calculated and it is found that they admit a resolution of the
identity and the spatial distribution of the wavefunction produces Lissajous
figures in correspondence with the classical 2:1 oscillator.
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