On the solution of the Schrödinger equation with time dependent boundary conditions

Resonant population transfer in the time-dependent quantum elliptical billiard

“…In contrast to the just described resonance, the broad double peak at ω = 15.6 and ω = 16.4 is mainly due to transitions between just two states. The corresponding population analysis yields p 4 and p 13 for ω = 15.6 and p 4 and p 18 for ω = 16.4, again in excellent agreement with the two-photon transition of E 4↔13 and the three-photon transition of E 4↔18 , see the greenish fields of table 2.…”

“…Recently, the dynamical properties of classical time-dependent two-dimensional billiards have attracted major attention, especially in the context of Fermi acceleration [1,2,3,4,5,6,7,8], which is defined as the unbounded energy gain of an ensemble of particles exposed to some external driving force [9]. Concerning the quantum dynamics of time-dependent billiards, there exist several studies investigating the quantum version of the one-dimensional Fermi-Ulam model (or variants of it) [10,11,12,13,14,15,16,17,18,19,20,21], but, to our knowledge, only two studies [22,23] investigate time-dependent billiards in higher dimensions.…”

“…The same time-law, that allows for analytic solutions, is found from a different perspective in Refs. [15,18] and by means of a supersymmetry formalism in Ref. [20].…”

Schrödinger Equation for a Non-Relativistic Particle in a Gravitational Field confined by Two Vibrating Mirrors

“…This adds another layer of complexity in the theoretical description with respect to the former setup. In fact, the qBOUNCE experiment constitutes a realization of a quantum mechanical system with time-dependent boundary conditions [1][2][3][4][5][6][7].…”

Time-dependent quantum graph

“…Treatment of such system requires solving the Schrödinger equation with time-dependent boundary conditions. Earlier, the problem of time-dependent boundary conditions in the Schrödinger equation has attracted much attention in the context of quantum Fermi acceleration [12][13][14], although different aspects of the problem were treated by many authors [16][17][18][19][20][21][22][23][24][25][26][27]. Detailed study of the problem can be found in a series of papers by Makowski and co-authors [21][22][23].…”