6533b85efe1ef96bd12bf4ee

RESEARCH PRODUCT

Non-isospectral Hamiltonians, intertwining operators and hidden hermiticity

Fabio Bagarello

subject

PhysicsQuantum PhysicsGeneral Physics and AstronomyFOS: Physical sciencesMathematical Physics (math-ph)Eigenvalues and eigenvectors of the second derivativeMathematics::Geometric Topologylaw.inventionGood quantum numbersymbols.namesakeintertwining relationsOperator (computer programming)IsospectralInvertible matrixlawQuantum electrodynamicssymbolsHamiltonian (quantum mechanics)Quantum Physics (quant-ph)Settore MAT/07 - Fisica MatematicaEigenvalues and eigenvectorsEigenvalue perturbationMathematical PhysicsMathematical physics

description

We have recently proposed a strategy to produce, starting from a given hamiltonian $h_1$ and a certain operator $x$ for which $[h_1,xx^\dagger]=0$ and $x^\dagger x$ is invertible, a second hamiltonian $h_2$ with the same eigenvalues as $h_1$ and whose eigenvectors are related to those of $h_1$ by $x^\dagger$. Here we extend this procedure to build up a second hamiltonian, whose eigenvalues are different from those of $h_1$, and whose eigenvectors are still related as before. This new procedure is also extended to crypto-hermitian hamiltonians.

yearjournalcountryeditionlanguage
2011-10-21
10.1016/j.physleta.2011.10.024http://arxiv.org/abs/1110.4828