Related papers: Particle in a box with a time-dependent $\delta$-f…
We consider the problem of computing, for a detector surface waiting for a quantum particle to arrive, the probability distribution of the time and place at which the particle gets detected, from the initial wave function of the particle in…
We analyze the non-relativistic problem of a quantum particle that bounces back and forth between two moving walls. We recast this problem into the equivalent one of a quantum particle in a fixed box whose dynamics is governed by an…
We study the quantum tunnelling of a very complex object of which only part is coupled to an external potential ( the potential barrier ). We treat this problem as the tunnelling of a particle (part of the system affected by the potential)…
An embedding method for solving the time-dependent Schr\"odinger equation is developed using the Dirac-Frenkel variational principle. Embedding allows the time-evolution of the wavefunction to be calculated explicitly in a limited region of…
Quantum mechanical scattering theory is studied for time-dependent Schroedinger operators, in particular for particles in a rotating potential. Under various assumptions about the decay rate at infinity we show uniform boundedness in time…
Exact solution of the Schr\"{o}dinger equation is given for a particle inside a hard sphere whose wall is moving with a constant velocity. Numerical computations are presented for both contracting and expanding spheres. The propagator is…
A solution of the scattering problem is obtained for the Schr\"odinger equation with the potential of induced dipole interaction, which decreases as the inverse square of the distance. Such a potential arises in the collision of an incident…
Exact solutions of time-dependent Schr\"odinger equation in presence of time-dependent potential is defined by point transformation and separation of variables. Energy and Heisenberg uncertainty relation are pursued for time-independent…
We establish that the exact quantum dynamics of a Brownian particle in the Caldeira-Leggett model can be mapped, at any temperature, onto a classical, non-Markovian stochastic process in phase space. Starting from a correlated thermal…
The solution of the time-dependent Schr\"odinger equation is discussed for a particle confined in half-space $x>0$ with a linear potential $V(x)=Kx$ in the following situations: (a) sudden removal of the wall and switching on the linear…
In this note we generalize entropy based on the quantum mechanical probability density distribution. Motivated by J. Munkhammar and the uncertainty of entropy we modified the origin wave function of the test particle. The corrected one…
Shannon entropy and Fisher information functionals are known to quantify certain information-theoretic properties of continuous probability distributions of various origins. We carry out a systematic study of these functionals, while…
The relationship between classical and quantum mechanics is explored in an intuitive manner by the exercise of constructing a wave in association with a classical particle. Using special relativity, the time coordinate in the frame of…
Using classical statistics, Schrodinger equation in quantum mechanics is derived from complex space model. Phase-space probability amplitude, that can be defined on classical point of view, has connections to probability amplitude in…
Studies of quantum fields and gravity suggest the existence of a minimal length, such as Planck length \cite{Floratos,Kempf}. It is natural to ask how the existence of a minimal length may modify the results in elementary quantum mechanics…
A global solution of the Schr\"odinger equation for explicitly time-dependent Hamiltonians is derived by integrating the non-linear differential equation associated with the time-dependent wave operator. A fast iterative solution method is…
Quantum pumping holds great potential for future applications in micro- and nanotechnology. Its main feature, dissipationless charge transport, is theoretically possible via several different mechanisms. However, since no unambiguous…
This study discusses the quantum behavior of a particle, which is controlled by fluctuations in the physical space-time (ST) variables, rather than provides a novel interpretation of quantum theory. The fluctuations, i.e., inhomogeneities…
Using the simplest but fundamental example, the problem of the infinite potential well, this paper makes an ideological attempt (supported by rigorous mathematical proofs) to approach the issue of…
In this article we have developed a formalism to obtain the Schr$\ddot{\rm{o}}$dinger equation for a particle in a frame undergoing an uniform acceleration in an otherwise flat Minkowski space-time geometry. We have presented an exact…