Abstract
The Equation of Motion Method is used in the spectral analysis of a non self-adjoint bosonic Hamiltonian acting on an infinite dimensional Hilbert space. The presented operator has real eigenvalues and can be diagonalized when it is expressed in terms of pseudo-bosons , which do not behave as ordinary bosons under the adjoint transformation, but obey the Weil-Heisenberg commutation relations.
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Acknowledgments
The authors are grateful to the Referee for valuable comments. This work was partially supported by the Centre for Mathematics of the University of Coimbra—UID/MAT/00324/2013, funded by the Portuguese Government through FCT/MEC and co-funded by the European Regional Development Fund through the Partnership Agreement PT2020.
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Bebiano, N., da Providência, J. (2016). The EMM and the Spectral Analysis of a Non Self-adjoint Hamiltonian on an Infinite Dimensional Hilbert Space. In: Bagarello, F., Passante, R., Trapani, C. (eds) Non-Hermitian Hamiltonians in Quantum Physics. Springer Proceedings in Physics, vol 184. Springer, Cham. https://doi.org/10.1007/978-3-319-31356-6_10
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DOI: https://doi.org/10.1007/978-3-319-31356-6_10
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