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## Non-isospectral Hamiltonians, intertwining operators and hidden hermiticity

Fabio Bagarello

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.

http://arxiv.org/abs/1110.4828
Mathematical Physics (math-ph); Quantum Physics (quant-ph)