Coherent states approach to Penning trap

Abstract

By using a matrix technique, which allows to identify directly the ladder operators, the Penning trap coherent states are derived as eigenstates of the appropriate annihilation operators. These states are compared with the ones obtained through the displacement operator. The associated wave functions and mean values for some relevant operators in these states are also evaluated. It turns out that the Penning trap coherent states minimize the Heisenberg uncertainty relation.

Asymmetric Penning trap coherent states

“…For this system we have finally shown that the annihilation operator coherent states become the same as the displacement operator coherent states. A final remark concerns the limit as the asymmetry parameter γ vanishes: since in this limit, our Hamiltonian becomes the one of the ideal Penning trap, all our results reduce to those obtained previously for the ideal Penning trap [14].…”

“…It is worth to remark that the asymmetric Penning trap becomes the ideal one [17]- [19] when the asymmetry parameter vanishes. In this way we can compare the results of this paper with those recently obtained for the ideal Penning trap [14]. This paper is organized as follows: in the following section several coherent states definitions will be presented.…”

“…Some of these definitions use as main ingredients the creation and annihilation operators as well as the system ground state [8]- [10]. However, there are interesting physical potentials which do not have any ground state at all, the identification of the creation and annihilation operators is not immediate, but a systematic technique to build up the corresponding CS is required anyway [11]- [14]. One of these systems, which we are going to address in this work, is the asymmetric Penning trap [15,16].…”

Time, Incompleteness and Singularity in Quantum Cosmology

“…People such as Hawking (1996Hawking ( , 1999 and Gold had assumed that all physical processes would go into reverse. In other words, they had assumed 6 Admittedly, this is a significant part of the epistemological argument put forth by Carroll and Carroll and Chen in the "natural" universe conjecture. Implicit in their theory is the idea that if cosmos formation is a "natural" phenomena, rather than the "unnatural" situation suggested by the differences in scale values for fundamental constants, then an additional, emergent force would be "unnatural".…”

Coherent States for the Asymmetric Penning Trap

“…However, there exist interesting physical potentials without a ground state for which the identification of the appropriate annihilation and creation operators is not automatic [10][11][12][13]. The system we are going to address in this work, the asymmetric Penning trap, belongs to this class [14,15].…”