Related papers: Quasi-conical quantum dot: electron states and qua…
We present an analysis of the two-dimensional Schrodinger equation for two electrons interacting via Coulombic force and confined in an anizotropic harmonic potential. The separable case of wy = 2wx is studied particularly carefully. The…
Perturbation theory, the quasiclassical approximation and the quantum surface of section method are combined for the first time. This solves the long standing problem of quantizing the resonances and chaotic regions generically appearing in…
A new type of basis functions is proposed to describe a two-electron continuum which arises as a final state in electron-impact ionization and double photoionization of atomic systems. We name these functions, which are calculated in terms…
In this paper, we investigate the Schr\"odinger equation for a class of spherically symmetric potentials in a simple and unified manner using the Lie algebraic approach within the framework of quasi-exact solvability. We illustrate that all…
The semiclassical Kepler-Coulomb problem and the quantum-mechanical Schr\"odinger-Coulomb problem are compared for their predictions of quadrupole E2 transitions. The semiclassical treatment involves an extension of previous work for the…
We analyze a class of quantum operations based on a geometrical representation of $d-$level quantum system (or qudit for short). A sufficient and necessary condition of complete positivity, expressed in terms of the quantum Fourier…
Extracting the Hamiltonian of interacting quantum-information processing systems is a keystone problem in the realization of complex phenomena and large-scale quantum computers. The remarkable growth of the field increasingly requires…
We present a new model for the study of spin-orbit coupling in interacting quasi-one-dimensional systems and solve it exactly to find the spectral properties of such systems. We show that the combination of spin-orbit coupling and…
Investigating localization properties of interacting disordered systems plays a crucial role in understanding thermalization and its absence in closed quantum systems. However, simulating such systems on classical computers is challenging…
We introduce a semiclassical quantization method which is based on a stroboscopic description of the classical and the quantum flows. We show that this approach emerges naturally when one is interested in extracting the energy spectrum…
The variational equation for the mean square displacement of the electron in the polaron worldline approach to quenched QED can be cast into a form which closely resembles the classical Abraham-Lorentz equation but without the conceptual…
We present a new dimensional scaling transformation of the Schrodinger equation for the two electron bond. This yields, for the first time, a good description of the two electron bond via D-scaling. There also emerges, in the large-D limit,…
A fourth-order Schr\"{o}dinger equation for the description of charge transport in semiconductors in the ballistic regime is proposed with the inclusion of non-parabolic effects in the dispersion relation in order to go beyond the simple…
A canonical transformation of a new type is offered as the mean for studying properties of a system of strongly correlated electrons. As an example of the utility of the transformation, it is used to demonstrate the existence of a quantum…
Dirac fermions interacting with a cylindrically symmetric quantum dot potential created in single and bilayer graphene are not confined but form quasi-bound states. The broadening of these quasi-bound states (i. e. the inverse of their…
We introduce the one-dimensional PT-symmetric Schrodinger equation, with complex potentials in the form of the canonical superoscillatory and suboscillatory functions known in quantum mechanics and optics. While the suboscillatory-like…
This paper is concerned with the efficient numerical treatment of 1D stationary Schr\"odinger equations in the semi-classical limit when including a turning point of first order. For the considered scattering problems we show that the wave…
Interacting fermions on a lattice can develop strong quantum correlations, which lie at the heart of the classical intractability of many exotic phases of matter. Seminal efforts are underway in the control of artificial quantum systems,…
We obtain dynamical lower bounds for some self-adjoint operators with pure point spectrum in terms of the spacing properties of their eigenvalues. In particular, it is shown that for systems with thick point spectrum, typically in Baire's…
We obtain analytic solution of the time-independent Schrodinger equation in two dimensions for a charged particle moving in the field of an electric quadrupole. The solution is written as a series in terms of special functions that support…