Coherent states for quadratic Hamiltonians

Details Coherent states for quadratic Hamiltonians Coherent states for quadratic Hamiltonians

2010-09-14

arxiv.org/abs/1009.2564v3

J. Phys. A 44: 035304,2011

Physics

Quantum Physics

19 pages, 1 figure, small changes. Accepted for publication in J. Phys. A: Math. Theor

Scientific paper

10.1088/1751-8113/44/3/035304

The coherent states for a set of quadratic Hamiltonians in the trap regime are constructed. A matrix technique which allows to identify directly the creation and annihilation operators will be presented. Then, the coherent states as simultaneous eigenstates of the annihilation operators will be derived, and they are going to be compared with those attained through the displacement operator method. The corresponding wave function will be found, and a general procedure for obtaining several expected values involving the canonical operators in these states will be described. The results will be illustrated through the asymmetric Penning trap.

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