Near coherent states of an electron in a time-dependent linear potential

Classical-quantum Interface of a Particle in a Time-dependent Linear Potential

“…The model on piecewise domains and the wave functions have been frequently used to model various physical systems [8,9]. Recent work [10][11][12][13][14][15][16][17][18][19][20][21][22] focus further on exact solutions and their properties and several method have been used to solve this system.…”

“…The model on piecewise domains and the wave functions have been frequently used to model various physical systems [8,9]. Recent work [10][11][12][13][14][15][16][17][18][19][20][21][22] focus further on exact solutions and their properties and several method have been used to solve this system.Using a particular unitary transformation operator, which resembles the one responsible for the existence of coherent states in harmonic oscillators, Song [22] relates the system of a particle in a linear potential to that of a free particle and found a general wave packet described by an Airy function. The Schrödinger equation for a free particle has also long been interesting in that the equation is formally identical to the wave equation of a beam of light in the paraxial approximation [23][24][25][26].…”

Solution of the Spinless Salpeter Equation with a Time-Dependent Linear Potential

“…Over past years, several papers have been written in connection with the quantum treatment of the problem describing a particle, in a one-dimensional world, subject to a time-dependent linear potential [1][2][3][4][5][6][7][8][9][10][11][12][13]. Indeed, besides its intrinsic mathematical interest, this model has various applications to many physical problems, such as, the quantum motion of trapped ions in the Paul trap [14,15], the motion of Brownian particles [16] and the transport of electrons in a strongly driven heterostructure [1,2].…”

“…The same types of solutions were also found by Feng [6] using a space-time transformation method. Recently, Lu et al [7] employed a test function method and reported an other set of n wave-packet-train solutions presenting a nearly squeezing coherence property. More recently, Berrehail et al [8] reexamined the problem in the context of LR and unitary transformation approaches and showed, in particular, how all known solutions can be related to each others.…”

Dynamics of Particle in Confined-Harmonic Potential in External Static Electric Field and Strong Laser Field

“…The Schrödinger equation has been solved for a particle in the general 1D time-dependent linear potential [12]. The quantum motion of an electron driven by a strong time-dependent linear potential in a 1D quantum wire has been investigated and interesting physical properties studied [13]. The possibility of exactly manipulating the quantum motional states of a single particle held in a double cosine potential by using laser beams has been explored [14].…”