Related papers: Numerical study of quantum mechanical systems usin…
An application of a quantum wave impedance method for a study of quantum-mechanical systems which con\-tain singular zero-range potentials is considered. It was shown how to reformulate the problem of an investigation of mentioned systems…
The method of a determination of a quantum wave impedance for an arbitrary piecewise constant potential was developed. On the base of this method both the well-known iterative formula \cite{Khondker_Khan_Anwar:1988} and alternative ways for…
We have developed the technique of a quantum wave impedance determination for the sequence of not only constant potentials but also for potentials of forms for which the solution of a Shr\"{o}dinger equation exists at least in terms of…
An analytical solution for a quantum wave impedance in a case of piesewise constant potential was derived. It is in fact an analytical depiction of a well-known iterative method of a quantum wave impedance determination. The expression for…
The relations between a quantum wave impedance function and elements of transfer and scattering matrixes for quantum mechanical systems with arbitrary localized form of potential were established. Obtained results allows using the…
Solutions to the stochastic wave equation on the unit sphere are approximated by spectral methods. Strong, weak, and almost sure convergence rates for the proposed numerical schemes are provided and shown to depend only on the smoothness of…
A method for a calculation of quantum capacitance for a two-dimesional electron gas (2DEG) in potential wells of complicated geometry on the base of a quantum wave impedance technique was proposed. The application of this method was…
A Bayesian approach is developed to determine quantum mechanical potentials from empirical data. Bayesian methods, combining empirical measurements and "a priori" information, provide flexible tools for such empirical learning problems. The…
The impedance measurement technique consists in that the phase-dependent (parametric) inductance of the system is probed by the classical tank circuit via measuring the voltage. The notion of the parametric inductance for the impedance…
Using a new Bayesian method for solving inverse quantum problems, potentials of quantum systems are reconstructed from coordinate measurements in non-stationary states. The approach is based on two basic inputs: 1. a likelihood model,…
The problem of quantum harmonic oscillator with "regular+random" square frequency, subjected to "regular+random external force, is considered in framework of representation of the wave function by complex-valued random process. Average…
Semiclassical methods are essential in analyzing quantum mechanical systems. Although they generally produce approximate results, relatively rare potentials exist for which these methods are exact. Such intriguing potentials serve as…
A numerical approach to the problem of wave scattering by many small particles is developed under the assumptions k<<1, d>>a, where a is the size of the particles and d is the distance between the neighboring particles. On the wavelength…
After the emergence of quantum mechanics and realising its need for an accurate understanding of physical systems, numerical methods were being used to undergo quantum mechanical treatment. With increasing system correlations and size,…
With the advent of gravitational wave detectors employing squeezed light, quantum waveform estimation---estimating a time-dependent signal by means of a quantum-mechanical probe---is of increasing importance. As is well known, backaction of…
A short introduction of a relation between a Green's function and a quantum wave impedance function as well as its application to a determination of eigenenergies and eigenfunctions of a quatum-mechanical system is provided. Three different…
During the past decades, quantum mechanical methods have undergone an amazing transition from pioneering investigations of experts into a wide range of practical applications, made by a vast community of researchers. First principles…
We investigate a numerical method for studying resonances in quantum mechanics. We prove rigorously that this method yields accurate approximations to resonance energies and widths for shape resonances in the semiclassical limit.
In many situations, one can approximate the behavior of a quantum system, i.e. a wave function subject to a partial differential equation, by effective classical equations which are ordinary differential equations. A general method and…
A nonparametric Bayesian approach is developed to determine quantum potentials from empirical data for quantum systems at finite temperature. The approach combines the likelihood model of quantum mechanics with a priori information over…