$C_{\lambda }$-extended harmonic oscillator and (para)supersymmetric quantum mechanics

Abstract

$C_{\lambda }$-extended oscillator algebras are realized as generalized deformed oscillator algebras. For $\lambda =3$, the spectrum of the corresponding bosonic oscillator Hamiltonian is shown to strongly depend on the algebra parameters. A connection with cyclic shape invariant potentials is noted. A bosonization of PSSQM of order two is obtained.

18 pages, LaTeX 2e

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• SU(2) and SU(1,1) Approaches to Phase Operators and Temporally Stable Phase States: Applications to Mutually Unbiased Bases and Discrete Fourier Transforms
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• Extended Weyl-Heisenberg algebra and Rubakov-Spiridonov superalgebra: Anyonic realizations
• Deformed $C_{\lambda }$-Extended Heisenberg Algebra in Non-commutative Phase-Space