Related papers: Energy spectrum design and potential function engi…
A method is proposed to find the wave function of an electron moving infinitely in the field of an arbitrary 1D layer structure with two different homogeneous semi-infinite boundaries. It is shown that in general the problem reduces to…
The optimized effective potential (OEP) method allows for calculation of the local, effective single particle potential of density functional theory for explicitly orbital-dependent approximations to the exchange-correlation energy…
We consider periodic energy problems in Euclidean space with a special emphasis on long-range potentials that cannot be defined through the usual infinite sum. One of our main results builds on more recent developments of Ewald summation to…
Due to the lack of the translational symmetry, calculating the energy spectrum of an incommensurate system has always been a theoretical challenge. Here, we propose a natural approach to generalize the energy band theory to the…
We obtain the effective potential at finite temperature within the left-right symmetric model. We take the Higgs sector to consist of two doublets and calculate its finite temperature effective potential up to the order of…
It is shown that the Schrodinger equation for a large family of pairs of two-dimensional quantum potentials possess wavefuctions for which the amplitude and the phase are interchangeable, producing two different solutions which are dual to…
The model of a spherical quantum dot with several donor impurities on its surface is suggested. The electron energy spectra are studied as a function of the quantum dot radius and the number of impurities. Several cases of the location of…
The general formulas to calculate the phase shifts of wave function of a particle scattering on a target formed by a pair of non-identical zero-range potentials are derived. It is shown that at asymptotically great distances from the target…
We analyze and clarify how the SGA (spectrum generating algebra) method has been applied to different potentials. We emphasize that each energy level $E_\nu$ obtained originally by Morse belongs to a {\em different} ${\mathfrak {so}}(2,1)$…
A simple methodology is suggested for the efficient calculation of certain central potentials having singularities. The generalized pseudospectral method used in this work facilitates {\em nonuniform} and optimal spatial discretization.…
We present a scalable approach to computing nonlinear balancing energy functions for control-affine systems with polynomial nonlinearities. Al'brekht's power-series method is used to solve the Hamilton-Jacobi-Bellman equations for…
For an arbitrary electromagnetic field, we define a prepotential $S$, which is a complex-valued function of spacetime. The prepotential is a modification of the two scalar potential functions introduced by E. T. Whittaker. The prepotential…
Baryons containing two heavy quarks are treated in the Born-Oppenheimer approximation. Schr\"odinger equation for two center Coulomb plus harmonic oscillator potential is solved by the method of ethalon equation at large intercenter…
We introduce a spectral density functional theory which can be used to compute energetics and spectra of real strongly--correlated materials using methods, algorithms and computer programs of the electronic structure theory of solids. The…
We describe a method for the calculation of accurate energy eigenvalues and expectation values of observables of separable quantum-mechanical models. We discuss the application of the approach to one-dimensional anharmonic oscillators with…
Existence of a spectral singularity (SS) in the spectrum of {a Schr\"{o}dinger operator with} a non-Hermitian potential requires exact matching of parameters of the potential. We provide a necessary and sufficient condition for a potential…
In this work, we provide a complete description of the scattering matrix elements and electron energy spectrum in one dimensional PT-symmetric hybrid finite systems, using the characteristic determinant approach. We present an analytical…
In this paper we derive an almost explicit analytic formula for asymptotic eigenenergy expansion of arbitrary odd degree polynomial potentials of the form $V(x)=(ix)^{2N+1}+\beta _{1}x^{2N}+\beta _{2}x^{2N-1}+\cdot \cdot \cdot \cdot \cdot…
A method, analogous to supersymmetry transformation in quantum mechanics, is developed for a particle in the lowest Landau level moving in an arbitrary potential. The method is applied to two-dimensional potentials formed by Dirac delta…
Experimental results from literature show equidistant energy levels in thin Bi films on surfaces, suggesting a harmonic oscillator description. Yet this conclusion is by no means imperative, especially considering that any measurement only…