Coherent states for the relativistic harmonic oscillator
1995
Recently we have obtained, on the basis of a group approach to quantization, a Bargmann-Fock-like realization of the Relativistic Harmonic Oscillator as well as a generalized Bargmann transform relating fock wave functions and a set of relativistic Hermite polynomials. Nevertheless, the relativistic creation and annihilation operators satisfy typical relativistic commutation relations of the Lie product (vector-z, vector-z(sup dagger)) approximately equals Energy (an SL(2,R) algebra). Here we find higher-order polarization operators on the SL(2,R) group, providing canonical creation and annihilation operators satisfying the Lie product (vector-a, vector-a(sup dagger)) = identity vector 1, the eigenstates of which are 'true' coherent states.
Keywords:
- Eigenvalues and eigenvectors
- Hermite polynomials
- Wave function
- Anharmonicity
- Harmonic oscillator
- Quantum harmonic oscillator
- Coherent states
- Quantum electrodynamics
- Commutation
- Mathematics
- Quantum mechanics
- Commutator
- Creation and annihilation operators
- Mathematical physics
- Operator (computer programming)
- Fock space
- Correction
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- Cite
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