Quantum systems with effective and time-dependent masses: form-preserving transformations and reality conditions

Abstract

Abstract:We study the time-dependent Schrödinger equation (TDSE) with an effective (position-dependent) mass, relevant in the context of transport phenomena in semiconductors. The most general form-preserving transformation between two TDSEs with different effective masses is derived. A condition guaranteeing the reality of the potential in the transformed TDSE is obtained. To ensure maximal generality, the mass in the TDSE is allowed to depend on time also.

Quantum features of molecular interactions associated with time-dependent non-central potentials

“…In effect, t m ( ) stands for effective mass that varies with time. Recently, molecular systems and other dynamical systems with time-dependent effective mass, as well as position-dependent effective mass, became a topic of research [7,37,40,[52][53][54][55][56][57][58][59][60]. In some cases, effective mass of a molecule in a system may vary through its interaction with the environment or various excitations such as energy, temperature, stress, pressure, phonon, etc.…”

Numerical solutions of the time‐dependent Schrödinger equation with position‐dependent effective mass

“…Most previous works in literature have focused on deriving analytic solutions or analytic approximations of solutions to such equations. For example, Serra and Lipparini [67] studied the equation with an effective (position-dependent) mass, relevant in the context of transport phenomena in semiconductors; Aktas and Sever [1] applied the point canonical transformation approach for systems with some spatially dependent effective masses, and exactly solvable potentials such as Morse, Pöschl-Teller (PT) and Hulthen, whose bound-state energies and corresponding wavefunctions are determined algebraically; Cobian and Schulze-Halberg [18] studied the Darboux transformation for the equation; Zhang et al [73] investigated the one-dimensional effective mass Schrödinger equation for PT-symmetric Scarf potential. They were accomplished by using an appropriate coordinate transformation to map the transformed exactly solvable one-dimensional Schrödinger equation with constant mass into the position-dependent mass equation; Bednarik and Cervenka [8] derived the exact solution to the problem with a polynomial mass as a linear combination of local Heun functions; and Jafarov et al [36] presented an exact solution of a confined model of the non-relativistic quantum harmonic oscillator, where the effective mass and the angular frequency depend on the position.…”

Feinberg-Horodecki states of a time-dependent mass distribution harmonic oscillator

“…is the maximum body size reached where Also, in this regard, Dantas et al have investigated the harmonic oscillator with timedependent mass along with frequency and a perturbative potential [10], Ji and Kim have found the exact quantum motions in the Heisenberg picture for a harmonic oscillator with time-dependent mass and frequency in terms of classical solutions [11], Maamache et al have generalized unitary equivalence and phase properties of the quantum parametric in harmonic oscillators [12], Axel Schulze-Halberg has studied the quantum systems with effective and time-dependent masses [13], Lai et al have investigated the many-body wave function of a quantum system with time-dependent effective mass, confined by a harmonic potential with time-dependent frequency, and perturbed by a time-dependent spatially homogeneous electric field [14]. Moya-Cessa and Fernandez Guasti have also studied the time dependent quantum harmonic oscillator that subjects to a sudden change of mass: continuous solution [15] and so forth.…”