Related papers: Convergence and completeness for square-well Stark…

We investigate the dynamics of a kicked particle in an infinite square well undergoing frequent measurements of energy. For a large class of periodic kicking force, constant diffusion is found in such a non-KAM system. The influence of…

The Kronig-Penney model describes what happens to electron states when a confining potential is repeated indefinitely. This model uses a square well potential; the energies and eigenstates can be obtained analytically for a the single well,…

Studies on symmetric extendibility of quantum states become especially important in a context of analysis of one-way quantum measures of entanglement, distilabillity and security of quantum protocols. In this paper we analyse composite…

From a careful study of the transcendental equations fulfilled by the bound state energies of a free particle in a quantum well, cylindrical wire or spherical dot with finite potential barrier, we have derived analytical expressions of…

In previous work, we derived the most general solution of the collisionless Boltzmann equation describing the accretion of a kinetic gas into a Schwarzschild black hole background, and we gave explicit expressions for the corresponding…

We consider the rationally extended exactly solvable Eckart potentials which exhibit extended shape invariance property. These potentials are isospectral to the conventional Eckart potential. The scattering amplitude for these rationally…

A new supersymmetry method for the generation of the quasi-exactly solvable (QES) potentials with two known eigenstates is proposed. Using this method we obtained new QES potentials for which we found in explicit form the energy levels and…

We have recently proposed a quantum control method based on the knowledge of the energy spectrum as a function of an external control parameter [Phys. Rev. Lett. {\bf 99}, 036806 (2007)]. So far, our method has been applied to connect the…

There exists a simple relationship between a quantum-mechanical bound-state wave function and that of nearby scattering states, when the scattering energy is extrapolated to that of the bound state. This relationship is demonstrated…

We study the energy properties of a particle in one dimensional semi-harmonic rectangular wells and barriers. The integration of energies is obtained by solving a simple transcendental equation. Scattering states are shown to include cases…

A general approach for constructing multidimensional quasi-exactly solvable (QES) potentials with explicitly known eigenfunctions for two energy levels is proposed. Examples of new QES potentials are presented.

We study the spectral convergence of compact, self-adjoint operators on a separable Hilbert space under operator norm perturbations, and derive asymptotic expansions for their eigenvalues and eigenprojections. Our analysis focuses on…

We provide a systematic study for the accretion of a collisionless, relativistic kinetic gas into a nonrotating black hole. To this end, we first solve the relativistic Liouville equation on a Schwarzschild background spacetime. The most…

Inspired by Lin-Pan-Wang (Comm. Pure Appl. Math., 65(6): 833-888, 2012), we continue to study the corresponding time-independent case of the Keller-Rubinstein-Sternberg problem. To be precise, we explore the asymptotic behavior of…

An exactly-solvable model of the non-relativistic harmonic oscillator with a position-dependent effective mass is constructed. The model behaves itself as a semi-infinite quantum well of the non-rectangular profile. Such a form of the…

We study fractional quantum Hall states in the cylinder geometry with open boundaries. By truncating the Coulomb interactions between electrons we show that it is possible to construct infinitely many exact eigenstates including the ground…

We study metastability for symbolic dynamic. We prove that for a global system given by two independent sub-systems linked by a hole, and for a Lipschitz continuous potential, the global equilibrium state converges, as the hole shrinks, to…

Using a first-principles classical many-body simulation of a Hall bar, we study the necessary conditions for the formation of the Hall potential: (i) Ohmic contacts with metallic reservoirs, (ii) electron-electron interactions, and (iii)…

Finding the entropy rate of Hidden Markov Processes is an active research topic, of both theoretical and practical importance. A recently used approach is studying the asymptotic behavior of the entropy rate in various regimes. In this…

Discrete PT-symmetric square wells are studied. Their wave functions are found proportional to classical Tshebyshev polynomials of complex argument. The compact secular equations for energies are derived giving the real spectra in certain…