Comment on “Wave functions of a time-dependent harmonic oscillator in a static magnetic field”

Noncommutative quantum mechanics in a time-dependent background

“…It should be noted here that our solution differs from those found in the literature [14,15]. As was pointed out in [15] the solutions provided in [14] are incorrect as they lead to time-dependent eigenvalues and thus contradict the basic foundations of the Lewis-Riesenfeld theory, i.e.…”

“…We notice that for θ(t) = 0 we can view this Hamiltonian with an appropriate identification of the remaining functions as describing a particle with mass m moving in an axially symmetric electromagnetic field, see section IV in [13]. It should also be noted that with a re-definition of the time-dependent coefficient attempts to solve the eigenvalue problem related to (2.3) can be found in the literature [14,15]. Unfortunately the solutions provided are partly incorrect or not useful for our purposes as we shall be commenting on below in more detail.…”

Lie algebraic approach to the time-dependent quantum general harmonic oscillator and the bi-dimensional charged particle in time-dependent electromagnetic fields

“…The linear potential, a particular case of the GHO, has been treated through powerful methods as the Lewis and Riesenfeld [30] invariant theory [36,37,38], Feynman's path integrals [39,40,41,42,43], the generalization of the well known ladder operators [44], Laplace transform techniques [45], time-space transformation methods [46] and others [47,48]. The charge particle in electromagnetic fields has been studied through different methods that include the Lewis and Riesenfeld [30] invariant theory [49,50], path integral method [51], unitary transformation approach [52,19], and through quadratic invariants [53].…”

“…Similarly to the GHO and the LP, the Hamiltonian describing a particle in time-dependent electromagnetic fields (CP) has countless applications in many physics fields such as quantum optics [43], single electron quantum dots [44] and magneto-transport theory [4,5]. This system has been studied through different methods that include the Lewis and Riesenfeld [24] invariant theory [45,46], path integral method [47], unitary transformation approach [17,48], and through quadratic invaritants [49].…”

Time evolution of two-dimensional quadratic Hamiltonians: A Lie algebraic approach

“…The isotropic harmonic oscillator in the presence of a time dependent magnetic field was investigated through the unitary transformation approach [22,51]. The Lewis and Riesenfeld invariant theory [34,52,53] and quadratic invariants [54] were applied to the study of a charged particle subject to time-varying electromagnetic fields [25].…”