Coherent States for the Asymmetric Penning Trap

Abstract

After identifying the appropriate ladder operators, the coherent states for the asymmetric Penning trap are derived as common eigenstates of the annihilation operators. They will be compared with the ones obtained by acting the displacement operator onto the extremal state, as well as with those which minimize some Heisenberg uncertainty relationships. The time evolution and relevant mean values for some operators in these states will be evaluated.

Coherent and Squeezed States: Introductory Review of Basic Notions, Properties, and Generalizations

“…A very interesting class of minimum wave packets was exhaustively studied by Nieto [142][143][144][145][146][147]. On the other hand, the dynamics of many physical systems can be described by using the quantum time-dependent harmonic oscillator [148][149][150][151][152][153][154][155][156][157][158], where the construction of minimum wave packets is relevant [159][160][161][162][163][164][165][166]. In a more general situation, wave packets with time-dependent width may occur for systems with different initial conditions, time-dependent frequency, or in contact with a dissipative environment [167][168][169][170].…”

Factorization method and new potentials from the inverted oscillator

“…This is because the new Hamiltonians are isospectral to the original one and the form of their potentials is quite similar. These facts, in particular, could be important to foresee alternative models for describing the small imperfections appearing when a real Penning trap is built up [5,45,46], specially if they do not change the spectrum of the corresponding ideal arrangement. Furthermore, we have studied the general algebraic structure of the original system with arbitrary ω, which is reduced to the harmonic oscillator case for ω = 1.…”

Exact Solutions of the Dirac Hamiltonian on the Sphere under Hyperbolic Magnetic Fields

“…Under these constraints, V 1 ef f can be obtained as given in (36). Now we can compare (35) and (36) using A i , i = 1, 2, ...6 given in [52]. These constants are given as [52] A…”

“…The Pauli Hamiltonian for a non-relativistic spin-1/2 particle possess N = 2 supersymmetry [33]. The Dirac equation and its analysis and discussion within super-symmetric quantum mechanics can be found in [34,35,36,37]. Moreover, extending a study of Bochner [38], exceptional orthogonal polynomials were introduced first in [39].…”