Evolution of Gaussian wave packet and nonadiabatic geometrical phase for the time-dependent singular oscillator

Abstract

The geometrical phase of a time-dependent singular oscillator is obtained in the framework of Gaussian wave packet. It is shown by a simple geometrical approach that the geometrical phase is connected to the classical Explicitly time-dependent problems present special difficulties in classical and quantum mechanics. However, they deserve detailed study because very interesting properties emerge when, even for simple linear systems, some parameters are allowed to vary with time. For instance, particular recent interest has been devoted to systems in which evolution originates geometric contributions [1][2][3][4][5][6]. One of these, the generalized harmonic oscillator has invoked much attention to study the nonadiabatic geometric phase for various quantum states, such as Gaussian, number, squeezed or coherent states, which can be found exactly [7][8][9][10]. Recently, the geometric phase for a cyclic wave packet solution of the generalized harmonic oscillator and its relation

Solution of the generalized Dirac equation in a time-dependent linear potential: Relativistic geometric amplitude factor

“…However, they deserve detailed study because very interesting properties emerge when, even for simple linear systems, some parameters are allowed to vary with time. For instance, particular recent interest has been devoted to the Schrödinger equation for timedependent potentials, mainly variable mass and frequency harmonic oscillators [1][2][3][4][5][6][7][8][9][10][11][12][13]. Besides the harmonic-oscillator potential model, the time-dependent linear potential has been frequently used in some others studies [14][15][16][17].…”

Quantum features of a charged particle in ionized plasma controlled by a time-dependent magnetic field

“…Hence the system is a kind of TDHSs that have attracted wide interest in the physical society [5,6,[17][18][19][20][21][22][23][24][25][26]. To derive quantum solutions of a TDHS, it is convenient to introduce an invariant operator [5,6] because the quantum properties of such system can be investigated via the eigenstates of the invariant operator.…”

Testing the validity of the Ehrenfest theorem beyond simple static systems: Caldirola–Kanai oscillator driven by a time-dependent force

“…A relationship between the quantum geometric phase and the classical Hannay angle has been found by Maamache and Bekkar. [1] Kim et al showed that the dispersions of quantum states do not depend on external forces. [2] A solution of the Schrödinger equation for a timedependent Hamiltonian system (TDHS) was obtained by Abdalla and Choi [3] and de Lima et al [4] using linear invariants and quadratic invariants.…”