Related papers: Quantum-wave evolution in a step potential barrier
The proper time of an observer can be introduced as a degree of freedom in quantum cosmology, additional to the existing fields. We review two arguments for using the Schr\"odinger equation to evolve the corresponding wavefunction. We…
We analytically compute the time evolution of an initial infinite plane wave in the presence of a 1-dimensional square quantum barrier. This calculation generalizes the analysis of the shutter problem and sets the basis for the calculation…
Branching flow -- a phenomenon known for steady wave propagation in two-dimensional weak correlated random potential is also present in the time-dependent Schr\"odinger equation for a single particle in one dimension, moving in a…
Even after decades of research the problem of first passage time statistics for quantum dynamics remains a challenging topic of fundamental and practical importance. Using a projective measurement approach, with a sampling time $\tau$, we…
A quantum finite multi-barrier system, with a periodic potential, is considered and exact expressions for its plane wave amplitudes are obtained using the Transfer Matrix method [10]. This quantum model is then associated with a stochastic…
We study the time-evolution of a quantum particle subjected to time-dependent zero-range forces in two dimensions. After establishing a conceivable ansatz for the solution to the Schr\"{o}dinger equation, we prove that the wave packet…
A phase space formulation of the filtering process upon an incident quantum state is developed. This formulation can explain the results of both quantum interference and delayed-choice experiments without making use of the controversial…
A research program within the scope of theories on "Emergent Quantum Mechanics" is presented, which has gained some momentum in recent years. Via the modeling of a quantum system as a non-equilibrium steady-state maintained by a permanent…
Evolution of a particle in an inverse square potential is studied. We derive an equation of motion for $\left<r^2\right>$ and solve it exactly. It gives us a possibility to identify the conditions under which a falling of a quantum particle…
We study the dynamics of a particle in continuous time and space, the displacement of which is governed by an internal degree of freedom (spin). In one definite limit, the so-called quantum random walk is recovered but, although quite…
We introduce a formalism for the calculation of the time of arrival t at a detector of particles traveling through interacting environments. We develop a general formulation that employs quantum canonical transformations from the free to…
We study the temporal formation of quantum mechanical bound states within a one-dimensional attractive square-well potential, by first solving the time-independent Schroedinger equation and then study a time dependent system with an…
We consider the quantum scattering off a time dependent barrier in one dimension. Our initial state is a right going eigenstate of the Hamiltonian at time t=0. It consists of a plane wave incoming from the left, a reflected plane wave on…
We analyze the time evolution describing a quantum source for noninteracting particles, either bosons or fermions. The growth behaviour of the particle number (trace of the density matrix) is investigated, leading to spectral criteria for…
In the B\"uttiker-Landauer perturbation approach to electron tunnelling, through a time-modulated rectilinear potential barrier, the Tien-Gordon identity was invoked, together with its infinite energy spectrum. Here, an exact treatment is…
For Schroedinger equations with both time-independent and time-dependent Kato potentials, we give a simple proof of the maximal speed bound. The latter states that the probability to find the quantum system outside the ball of radius…
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…
The main purpose of the paper is an essentially probabilistic analysis of relativistic quantum mechanics. It is based on the assumption that whenever probability distributions arise, there exists a stochastic process that is either…
In quantum physics, disturbance due to a measurement is not negligible. This requires the time parameter $t$ in the Schr\"odinger or Heisenberg equation to be considered differently from a time continuum of experimenter's clock $T$ on which…
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…