Abstract
These notes are based on a simple remark, which appeared more and more evident during my recent attempts to use coherent states in the computation of some transition probabilities for some specific quantum mechanical systems driven by non self-adjoint Hamiltonians.
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Notes
- 1.
In fact, the BCH formula is something more general. It involves the equality e Z = e X e Y, where X, Y and Z are all operators. However, in view of our interest in coherent states, we will call BCH formula the one in which X and Y are proportional to ladder operators of some kind, like c and c †, or other ladder operators we are going to consider in the following.
References
F. Bagarello, Deformed canonical (anti-)commutation relations and non Hermitian Hamiltonians, in Non-selfadjoint Operators in Quantum Physics: Mathematical Aspects, ed. by F. Bagarello, J.P. Gazeau, F.H. Szafraniec, M. Znojil (Wiley, New York, 2015)
F. Bagarello, J. Feinberg, Bicoherent-state path integral quantization of a non-Hermitian Hamiltonian. Ann. Phys. 422, 168313 (2020)
M. Combescure, R. Didier, Coherent States and Applications in Mathematical Physics (Springer, Cham, 2012)
B.C. Hall, Quantum Theory for Mathematicians (Springer, New York 2013)
A.M. Perelomov, Generalized Coherent States and Their Applications (Springer, Berlin, 1986)
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Bagarello, F. (2022). Introduction. In: Pseudo-Bosons and Their Coherent States. Mathematical Physics Studies. Springer, Cham. https://doi.org/10.1007/978-3-030-94999-0_1
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DOI: https://doi.org/10.1007/978-3-030-94999-0_1
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