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)