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Recent theoretical calculations, demonstrating that quantized charge transfer due to adiabatically modulated potentials in mesoscopic devices can result purely from the interference of the electron wave functions (without invoking…
We present a phase space formulation of quantum mechanics in the Schr\"odinger representation and derive the associated Weyl pseudo-differential calculus. We prove that the resulting theory is unitarily equivalent to the standard…
An infinite sequence of potential well functions is considered. A numerical method is used for the Schr$\ddot{\text{o}}$dinger equation to obtain the energy eigenvalue spectra for a number of these potential well functions. The results for…
We perform quantum mechanically exact calculations of resonances in the spectrum of the hydrogen atom in crossed external fields and establish a close connection between the classical transition state in phase space and features in the…
We investigate transmission properties of triple barrier parabolic double quantum well structure using the non-equilibrium Green's function method. In particular, we examine the effect of system parameters on transmission coefficient. The…
The Schr\"odinger-like equations for the marginal and conditional probability amplitudes resulting from the exact factorization of the wavefunction of a two-component system are derived in a form that is invariant to gauge and coordinate…
We derive the Schroedinger equation for a spinless charged particle constrained to a curved surface with electric and magnetics fields applied. The particle is confined on the surface using a thin-layer procedure, giving rise to the…
From a careful study of the transcendental equations fulfilled by the bound state energies of a free particle in a quantum well, cylindrical wire or spherical dot with finite potential barrier, we have derived analytical expressions of…
We study the energy properties of a particle in one dimensional semi-harmonic rectangular wells and barriers. The integration of energies is obtained by solving a simple transcendental equation. Scattering states are shown to include cases…
In this article we focus on a semiclassical Schr\"odinger equation with matrix-valued potential presenting a symmetric conjoint crossing of three eigenvalues. The potential we consider is well-known in the chemical literature as a pseudo…
The relationship between the threshold energy for a deep sub-barrier fusion hindrance phenomenon and the energy at which the regime of interaction changes (the turning-off of the nuclear forces and friction) in the sub-barrier capture…
The stationary nonlinear Schr\"odinger equation (or Gross-Pitaevskii equation) for one-dimensional potential scattering is studied. The nonlinear transmission function shows a distorted profile, which differs from the Lorentzian one found…
In this paper we revisit the one-dimensional tunneling problem. We consider Kemble's approximation for the transmission coefficient. We show how this approximation can be extended to above-barrier energies by performing the analytical…
Understanding compressible turbulence is critical for modeling atmospheric, astrophysical, and engineering flows. However, compressible turbulence poses a more significant challenge than incompressible turbulence. We present a novel…
We construct the Green functions (or Feynman's propagators) for the Schroedinger equations of the form $i\psi_{t}+{1/4}\psi_{xx}\pm tx^{2}\psi =0$ in terms of Airy functions and solve the Cauchy initial value problem in the coordinate and…
Classical transport equations with probabilistic initial conditions can be viewed as quantum systems. In a discrete version they are probabilistic automata. The time-local probabilistic information is encoded in a classical wave function.…
We numerically implement the reactive flux formalism on the basis of a recently proposed c-number Langevin equation [Barik \textit{et al}, J. Chem. Phys. {\bf 119}, 680 (2003); Banerjee \textit{et al}, Phys. Rev. E {\bf 65}, 021109 (2002)]…
Others have solved the Schr\"odinger equation for a one-dimensional model having a square potential barrier in free-space by requiring an incident and a reflected wave in the semi-infinite pre-barrier region, two opposing waves in the…
We obtain exact solutions of the 2D Schr\"odinger equation for Hydrogen atom with the lenear and Harmonic Potentials in noncommutative complex space, using the Power-series expansion method. Hence we can say that the Schr\"odinger equation…
Analytical solutions of the Schrodinger equation are obtained for some diatomic molecular potentials with any angular momentum. The energy eigenvalues and wave functions are calculated exactly. The asymptotic form of the equation is also…