Related papers: Triangular Quantum Profiles: transmission probabil…
We discuss a pairwise-comparison viewpoint on finite families of qubit states. Starting from transition amplitudes between pure states, we distinguish three associated levels of comparison data: complex amplitudes, transition probabilities,…
The equations for the amplitudes of transition probabilities are found. The resonance frequency of the system is calculated. It is shown the dependence of the resonance frequency on the initial transverse coordinate of an electron. This…
We introduce the third independent exactly solvable hypergeometric potential, after the Eckart and the P\"oschl-Teller potentials, which is proportional to an energy-independent parameter and has a shape that is independent of this…
Solutions of the time-dependent Schr\"odinger equation are mapped to other solutions for a (possibly) different potential by so-called form-preserving transformations. These time-dependent transformations of the space and time coordinates…
The von Neumann evolution equation for density matrix and the Moyal equation for the Wigner function are mapped onto evolution equation for optical tomogram of quantum state. The connection with known evolution equation for symplectic…
We investigate the evolution of an electron undergoing coherent tunneling via adiabatic passage (CTAP) using the solution of the one-dimensional Schroedinger equation in both space and time for a triple well potential. We find the…
Using Gaussian wave packet solutions, we examine how the kinetic energy is distributed in time-dependent solutions of the Schrodinger equation corresponding to the cases of a free particle, a particle undergoing uniform acceleration, a…
A superspace version of the Schr\"odinger equation with a delta potential is studied using Fourier analysis. An explicit expression for the energy of the single bound state is found as a function of the super-dimension M in case M is…
It is shown that a class of approximate resonance solutions in the three-body problem under the Newtonian gravitational force are equivalent to quantized solutions of a modified Schr\"odinger equation for a wide range of masses that…
The transfer-matrix methodology is used to solve linear systems of differential equations, such as those that arise when solving Schr\"odinger's equation, in situations where the solutions of interest are in the continuous part of the…
A new solvable hyperbolic single wave potential is found by expanding the regular solution of the 1D Schr\"odinger equation in terms of square integrable basis. The main characteristic of the basis is in supporting an infinite tridiagonal…
The semiclassical Kepler-Coulomb problem and the quantum-mechanical Schr\"odinger-Coulomb problem are compared for their predictions of quadrupole E2 transitions. The semiclassical treatment involves an extension of previous work for the…
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…
The tunneling effect of a periodic potential with an asymmetric twin barrier per period is calculated using the instanton method. The model is derived from the Hamiltonian of a small ferromagnetic particle in an external magnetic field…
A known limitation of time-dependent mean-field approaches is a lack of quantum tunneling for collective motions such as in sub-barrier fusion reactions. As a first step toward a solution, a time-dependent model is considered using a…
The coherence properties of the classical waves are discussed in terms of the Cauchy problem for the wave equation, and of a discrete representation by an ensemble of Hamiltonian systems. Wave quanta are related to specific "action fields",…
We calculate the single-particle momentum distribution of a quantum many-particle system in the presence of the Coulomb interaction and a confining potential. The region of intermediate momenta, where the confining potential dominates,…
We report a method to derive the potential barrier profile shape in a dynamic quantum dot and show the loading statistics, and hence accuracy of electron transfer, depend significantly on the shape of the barrier. This method takes a…
We investigate the transition radiation on a periodically deformed interface between two dielectric media. Under the assumption that the dielectric permittivities of the media are close, a formula is derived for the spectral-angular…
Time-dependent quantum mechanics provides an intuitive picture of particle propagation in external fields. Semiclassical methods link the classical trajectories of particles with their quantum mechanical propagation. Many analytical results…