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Motivated by our recent work published in [23] , we achieve, in this paper, a matrix formulation of the density operator to construct a two-component vector coherent state representation for a supersymmetric harmonic oscillator. We investigate and discuss the main relevant statistical properties. We use the completeness relation to perform the thermodynamic analysis in the diagonal P-representation of the density operator. [ABSTRACT FROM AUTHOR]

The density operator representation in the context of multi-matrix vector coherent states basis is performed and applied to Landau levels of an electron in an electromagnetic field coupled to an isotropic harmonic potential. Main relevant statistical properties such as the Mandel Q -parameter and the signal-to-quantum-noise ratio are derived and discussed. The Q -Husimi distribution is also investigated from the viewpoint of the Glauber-Sudarshan- P representation of the density operator. [ABSTRACT FROM AUTHOR]

Abstract: This paper stands for a logic continuation of the previous work [A. Ronveaux, Factorization of the Heun’s differential operator, Appl. Math. Comput. 141 (2003) 177–184]. We propose a factorization of the confluent, double confluent and biconfluent Heun’s differential equations and investigate their solutions. [Copyright &y& Elsevier]