A Swanson-like Hamiltonian and the inverted harmonic oscillator
- 13 May 2022
- journal article
- research article
- Published by IOP Publishing in Journal of Physics A: Mathematical and Theoretical
- Vol. 55 (22) , 225204
Abstract
We deduce the eigenvalues and the eigenvectors of a parameter-dependent Hamiltonian H θ which is closely related to the Swanson Hamiltonian, and we construct bi-coherent states for it. After that, we show how and in which sense the eigensystem of the Hamiltonian H of the inverted quantum harmonic oscillator can be deduced from that of H θ . We show that there is no need to introduce a different scalar product using some ad hoc metric operator, as suggested by other authors. Indeed we prove that a distributional approach is sufficient to deal with the Hamiltonian H of the inverted oscillator.Keywords
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