We use the Lewis-Riesenfeld theory to determine the exact form of the wavefunctions of a two-dimensionnal harmonic oscillator with time-dependent mass and frequency in presence of the Aharonov-Bohm effect (AB). We find that the auxiliary equation is independent of the AB magnetic flux. In the particular case of quantized AB magnetic flux the wavefunctions coincide exactly with the wavefunctions of the 2D time-dependent harmonic oscillator.KEY WORDS: harmonic oscillator; magnetic field; Aharonov-Bohm effect; exact wave function.PACS: 03.65Ge; 03.65Fd; 03.65Bz.In the last few decades the problem of time-dependent systems have played a major role in the study of several physics phenomena (Chung-In et al., 2002;Kleber, 1994;Markov, 1989). A great deal of attention has been paid to some specific problems of time-dependent oscillators among them the time-dependent singular oscillator. In fact this specific problem has been studied extensively in different direction by many authors by whom closed-form solutions are obtained in explicit form (Dodonov et al.). The construction of the invariant (Lewis and Riesenfeld, 1969) (constants of the motion), has attracted much attention, which describe a quantum system governed by a time-dependent Hamiltonian. Lewis and Riensenfeld (Lewis and Riesenfeld, 1969) have shown that, if the system admits an invariant I (t), it is possible to find a privileged basis of eigenstates of this operator when multiplied
We use the Lewis–Riesenfeld theory to determine the exact form of the wavefunctions of a two-dimensional Pauli equation of a charged spin 1∕2 particle with time-dependent mass and frequency in the presence of the Aharonov–Bohm effect and a two-dimensional time-dependent harmonic oscillator. We find that the irregular solution at the origin as well as the regular one contributes to the phase of the wavefunction.
We introduce a pseudo-squeezed bosonic ladder operator defined as a time-dependent non-Hermitian linear invariant and related to their adjoint operators via the bounded Hermitian invertible operator or metric operator. In fact, they are obtained from the squeezed transformation of the pseudo-bosons annihilation and creation operators. Thus, the pseudo-bosonic squeezed coherent states are just obtained as pseudo-displacement operator method acting on the ground pseudo-squeezed state. To our knowledge, the time-dependent pseudo-squeezed coherent states have not been constructed until now. As an illustration, we study the time-dependent non-Hermitian displaced harmonic oscillator, and the properties of these states are analysed with respect to the localization in position and to uncertainty principle.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.