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The approximate numerical method for a calculation of a quantum wave impedance in a case of a potential energy with a complicated spatial structure is considered. It was proved that the approximation of a real potential by a piesewise…
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 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…
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 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…
We derive analytic expressions of the recursive solutions to the Schr\"{o}dinger's equation by means of a cutoff potential technique for one-dimensional piecewise constant potentials. These solutions provide a method for accurately…
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…
On the base of a 1D Shr\"{o}dinger equation the non-linear first-order differential equation (Ricatti type) for a quantum wave impedance function was derived. The advantages of this approach were discussed and demonstrated for a case of a…
An differential equation for wave functions is proposed, which is equivalent to Schr\"{o}dinger's wave equation and can be used to determine energy-level gaps of quantum systems. Contrary to Schr\"{o}dinger's wave equation, this equation is…
Exact analytic solutions to the Schr\"odinger equation for an electron moving in three dimensional potentials have been studied. These solutions can correspond to metals, semiconductors, or insulators. We show that there is an efficient…
Using the method of the "exact discretization" of the Schr\"odinger equation, we propose a particular discretized version of the N=2 Supersymmetric Quantum Mechanics. After defining the corresponding shape invariance condition, we show that…
A simple and explicit technique for the numerical solution of the two-particle, time-dependent Schr\"{o}dinger equation is assembled and tested. The technique can handle interparticle potentials that are arbitrary functions of the…
In quantum physics, the theoretical study of unbound many-body systems is typically quite complex -- owing to the combination of their large spatial extension and the so-called {\it curse of dimensionality}. Often, such systems are studied…
To study the ballistic transport of charge carriers in nano-structured quantum devices, a highly efficient numerical technique is developed, which provides continuous transmission spectra for arbitrarily complex potential geometries in two…
A new proof is given of the existence of the solution to electromagnetic (EM) wave scattering problem for an impedance body of an arbitrary shape. The proof is based on the elliptic systems theory and elliptic estimates for the solutions of…
An algebraic approach to the study of quantum mechanics on configuration spaces with a finite fundamental group is presented. It uses, in an essential way, the Gelfand-Naimark and Serre-Swan equivalences and thus allows one to represent…
A theory for wave mechanical systems with local inversion and translation symmetries is developed employing the two-dimensional solution space of the stationary Schr\"odinger equation. The local symmetries of the potential are encoded into…
This paper discusses the practical development of space-time boundary element methods for the wave equation in three spatial dimensions. The employed trial spaces stem from simplex meshes of the lateral boundary of the space-time cylinder.…
Quantum mechanical tunneling across smooth double barrier potentials modeled using Gaussian functions, is analyzed numerically and by using the WKB approximation. The transmission probability, resonances as a function of incident particle…
Schr\"odinger operator on half-line with complex potential and the corresponding evolution are studied within perturbation theoretic approach. The total number of eigenvalues and spectral singularities is effectively evaluated. Wave…