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We present a conditionally exactly solvable singular potential for the one-dimensional Schr\"odinger equation which involves the exactly solvable inverse square root potential. Each of the two fundamental solutions that compose the general…
We study a quantum computer with fixed and permanent interaction of diagonal type between qubits. It is controlled only by one-qubit quick transformations. It is shown how to implement Quantum Fourier Transform and to solve Shroedinger…
We discussed exact solutions of the Schroedinger equation for a two-dimensional parabolic confinement potential in a homogeneous external magnetic field. It turns out that the two-electron system is exactly solvable in the sense, that the…
Electron spins in semiconductor quantum dots are good candidates of quantum bits for quantum information processing. Basic operations of the qubit have been realized in recent years: initialization, manipulation of single spins, two qubit…
A simple real-space model for the electron wavefunction is suggested, based on a transverse wave with helicity, rotating at mc^2/h. The mapping of the real two-dimensional vector phasor to the complex plane permits this to satisfy the…
The goal of this paper is to construct an effective model for studying the asymptotic solution of the scattering problem of three one-dimensional quantum particles with finite (short-range) attractive pair potentials. The asymptotic nature…
A simple real-space model for the free-electron wavefunction with spin is proposed, based on coherent vortices on the scale of h/mc, rotating at mc^2/h. This reproduces the proper values for electron spin and magnetic moment. Transformation…
In this article we show that separation of variables for second-order superintegrable systems in two-dimensional Euclidean space generates both exactly solvable (ES) and quasi-exactly solvable (QES) problems in quantum mechanics. In this…
We generalize the textbook Kronig-Penney model to realistic conditions for a quantum-particle moving in the quasi-one-dimensional (quasi-1D) waveguide, where motion in the transverse direction is confined by a harmonic trapping potential.…
A quantum computing circuit is presented that approximates a single spin wave quantum on a linear chain of spin 1/2 particles described by a Heisenberg Hamiltonian. The circuit is a product state where each qubit represents a spin. The spin…
he properties of excitons formed in spherical quantum dots are studied using the $\mathbf{k}\cdot\mathbf{p}$ method within the Hartree approximation. The spherical quantum dots considered have a central core and several concentric layers of…
In this work we define a formal notion of a quantum phase crossover for certain Bethe ansatz solvable models. The approach we adopt exploits an exact mapping of the spectrum of a many-body integrable system, which admits an exact Bethe…
We present a model to find analytically the electronic states in self-assembled quantum dots with a truncated spherical cap (`lens') geometry. A conformal analytical image is designed to map the quantum dot boundary into a dot with…
The molecular Schr\"odinger equation is rewritten in terms of non-unitary equations of motion for the nuclei (or electrons) that depend parametrically on the configuration of an ensemble of generally defined electronic (or nuclear)…
We investigate a system of three tunnel-coupled semiconductor quantum dots in a triangular geometry, one of which is connected to a metallic lead, in the regime where each dot is essentially singly occupied. Both ferro- and…
We develop a modified semi-classical approach to the approximate solution of Schrodinger's equation for certain nonlinear quantum oscillations problems. At lowest order, the Hamilton-Jacobi equation of the conventional semi-classical…
We study the dynamics of a molecule's nuclear wave-function near an avoided crossing of two electronic energy levels, for one nuclear degree of freedom. We derive the general form of the Schroedinger equation in the n-th superadiabatic…
We use variable transformation from the real line to finite or semi-infinite spaces where we expand the regular solution of the 1D time-independent Schrodinger equation in terms of square integrable bases. We also require that the basis…
We present a new exactly solvable quantum problem for which the Schroedinger equation allows for separation of variables in oblate spheroidal coordinates. Namely, this is the quantum mechanical two Coulomb centers problem for the case of…
Quantum Selected Configuration Interaction (QSCI) and an extended protocol known as Sample-based Quantum Diagonalization (SQD) have emerged as promising algorithms to solve the electronic Schr\"odinger equation with noisy quantum computers.…