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New coherent states for the BDS-Hamiltonian

Domenii publicaţii > Fizica + Tipuri publicaţii > Articol în revistã ştiinţificã

Autori: Dusan Popov

Editorial: Czechoslovak Journal of Physics, 52 (9), p.993 -1010, 2002.


In the paper we construct a new set of coherent states for a deformed
Hamiltonian of the harmonic oscillator, previously introduced by Beckers, Debergh, and Szafraniec,
which we have called the BDS-Hamiltonian. This Hamiltonian depends on the new creation operator, i.e. the usual creation operator displaced with the real quantity lambda. In order to construct the coherent states, we use a new measure in the Hilbert space of the Hamiltonian eigenstates, in fact we change the inner product. This ansatz assures that the set of eigenstates be orthonormalized and complete. In the new inner product space the BDS-Hamiltonian is self-adjoint. Using these coherent states, we construct the corresponding
density operator and we find the P-distribution function of the unnormalized density operator of the BDS-Hamiltonian. Also, we calculate some thermal averages related to
the BDS-oscillators system which obey the quantum canonical distribution conditions.

Cuvinte cheie: coherent states, density matrix