Related papers: Square-Well Approximation for the Anharmonic and t…
A set of effective equations for the gauge-invariant gravitational perturbations in the interior of a spherically symmetric, non-rotating black hole is derived within the framework of hybrid loop quantum cosmology. The quantum zero-mode of…
In this paper we discuss two methods of resumming the leading and next to leading order in 1/N diagrams for the quartic O(N) model. These two approaches have the property that they preserve both boundedness and positivity for expectation…
In this paper we introduce a generalization to the algebraic Bender-Wu recursion relation for the eigenvalues and the eigenfunctions of the anharmonic oscillator. We extend this well known formalism to the time-dependent quantum statistical…
A simple method for the calculation of higher orders of the logarithmic perturbation theory for bound states of the spherical anharmonic oscillator is developed. The structure of the perturbation series for energy eigenvalues of the sextic…
We discuss two simple variational approaches to quantum wells. The trial harmonic functions analyzed in an earlier paper give reasonable results for all well depths and are particularly suitable for deep wells. On the other hand, the…
We find the leading electroweak corrections to the Lagrangians of heavy-quark effective theory and nonrelativistic QCD. These corrections appear in the Wilson coefficients of the two- and four-quark operators and are considered here at…
The study of the convergence of power series expansions of energy eigenvalues for anharmonic oscillators in quantum mechanics differs from general understanding, in the case of quasi-exactly solvable potentials. They provide examples of…
This paper is devoted to study the energy problem in general relativity using approximate Lie symmetry methods for differential equations. We evaluate second-order approximate symmetries of the geodesic equations for the stringy charged…
The results of systematic experimental studies of quantum oscillations of resistivity, Hall coefficient and capacitance in GaAs and In$_x$Ga$_{1-x}$As quantum wells (QWs) with a simple electron spectrum and HgTe QWs with a complicated…
This paper present how to solve the problem of cylindrical quantum wells with potential energy different from zero and with singularity of the energy on the axis of the cylinder. The solution to the problem was obtained using methods of…
A new approach to nonperturbative calculations in quantum electrodynamics is proposed. The approach is based on a regular iteration scheme for solution of Schwinger-Dyson equations for generating functional of Green functions. The approach…
Adiabatic quantum computing is implemented on specialized hardware using the heuristics of the quantum annealing algorithm. This setup requires the addressed problems to be formatted as discrete quadratic functions without constraints and…
One dimensional quantum mechanics problems, namely the infinite potential well, the harmonic oscillator, the free particle, the Dirac delta potential, the finite well and the finite barrier are generalized for finite arbitrary dimension in…
We show that standard next-to-leading order (NLO) perturbative QCD analyses used to extract $\alpha_{s}$ from LEP data do not serve to disentangle the completely unknown renormalization scheme (RS) invariant next-NLO (NNLO) and higher-order…
A method is described to solve the nonlinear Langevin equations arising from quadratic interactions in quantum mechanics. While, the zeroth order linearization approximation to the operators is normally used, here first and second order…
It is shown that for the one-dimensional quantum anharmonic oscillator with potential $V(x)= x^2+g^2 x^4$ the Perturbation Theory (PT) in powers of $g^2$ (weak coupling regime) and the semiclassical expansion in powers of $\hbar$ for…
Quantum Approximate Optimization Algorithm (QAOA) and Quantum Annealing are prominent approaches for solving combinatorial optimization problems, such as those formulated as Quadratic Unconstrained Binary Optimization (QUBO). These…
Garrett's approximation for the calculation of bound states energy in square wells is applied in a consistent way. So, one obtains simple formulas for these energies, with errors of about 1% for moderate, and 0.01% for deep wells. The…
This paper investigates the performance of the emerging non-variational Quantum Walk-based Optimisation Algorithm (NV-QWOA) for solving small instances of the Quadratic Assignment Problem (QAP). NV-QWOA is benchmarked against classical…
The linewidths and the energy shifts of the resonant states of the impurity electron in GaAs-based quantum wells (QWs) with infinite barriers are calculated. The two-dimensional Schr\"{o}dinger equation for the charge impurity in the QW is…