6533b82efe1ef96bd1292909
RESEARCH PRODUCT
Intertwining operators for non-self-adjoint hamiltonians and bicoherent states
Fabio Bagarellosubject
Pure mathematicsQuantum Physics010308 nuclear & particles physicsHilbert spaceFOS: Physical sciencesStatistical and Nonlinear PhysicsMathematical Physics (math-ph)01 natural sciencesMechanical systemsymbols.namesake0103 physical sciencessymbols010306 general physicsHamiltonian (quantum mechanics)Quantum Physics (quant-ph)QuantumSettore MAT/07 - Fisica MatematicaSelf-adjoint operatorEigenvalues and eigenvectorsMathematical PhysicsMathematicsStatistical and Nonlinear Physicdescription
This paper is devoted to the construction of what we will call {\em exactly solvable models}, i.e. of quantum mechanical systems described by an Hamiltonian $H$ whose eigenvalues and eigenvectors can be explicitly constructed out of some {\em minimal ingredients}. In particular, motivated by PT-quantum mechanics, we will not insist on any self-adjointness feature of the Hamiltonians considered in our construction. We also introduce the so-called bicoherent states, we analyze some of their properties and we show how they can be used for quantizing a system. Some examples, both in finite and in infinite-dimensional Hilbert spaces, are discussed.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2016-01-01 |