Mathematical aspects of intertwining operators: the role of Riesz bases

Abstract

In this paper we continue our analysis of intertwining relations for both self-adjoint and not self-adjoint operators. In particular, in this last situation, we discuss the connection with pseudo-hermitian quantum mechanics and the role of Riesz bases.

Journal of Physics A, in press

References in corpus (5)

• Pseudo-bosons, Riesz bases and coherent states
• Quons, coherent states and intertwining operators
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• Nonlinear Supersymmetric Quantum Mechanics: concepts and realizations
• Examples of Pseudo-bosons in quantum mechanics
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• More mathematics for pseudo-bosons
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• Pseudo-bosons, so far
• Non linear pseudo-bosons
• Non linear pseudo-bosons versus hidden Hermiticity. II: The case of unbounded operators
• Hamiltonians defined by biorthogonal sets
• Intertwining operators for non self-adjoint Hamiltonians and bicoherent states
• Non linear pseudo-bosons versus hidden Hermiticity
• $\mathcal{D}$ pseudo-bosons in quantum models
• A chain of solvable non-Hermitian Hamiltonians constructed by a series of metric operators
• Damping and Pseudo-fermions
• Non self-adjoint Hamiltonians with complex eigenvalues
• Dissipation evidence for the quantum damped harmonic oscillator via pseudo-bosons
• Non-isospectral Hamiltonians, intertwining operators and hidden hermiticity
• Heisenberg dynamics for non self-adjoint Hamiltonians: symmetries and derivations
• Two-parameters pseudo-bosons