In this work, the canonical transformation method is applied to a general second order differential equation (DE) in order to trasform it into a Schrödinger-like DE. Our proposal is based on an auxiliary function g(x) which determines the transformation needed to find exactly-solvable potentials associated to a known DE. To show the usefulness of the proposed approach, we consider explicitly th...

The concept of quantum monodromy is introduced to give insight into the energy levels of systems with cylindrically symmetrical potential energy barriers. The K structure of bending progressions of bent molecules and the pendular states of dipolar molecules in strong electric ® elds are taken as molecular examples. Results are given for a two-dimensional champagne bottle model, for six computed...

We investigate the controllability of quantum electrons trapped in a twodimensional device, typically a MOS field-effect transistor. The problem is modeled by the Schrödinger equation in a bounded domain coupled to the Poisson equation for the electrical potential. The controller acts on the system through the boundary condition on the potential, on a part of the boundary modeling the gate. We ...

For any module over the affine Weyl group we construct a representation of the associated trigonometric Cherednik algebra A(k) at critical level in terms of Dunkl type operators. Under this representation the center of A(k) produces quantum conserved integrals for root system generalizations of quantum spin-particle systems on the circle with delta function interactions. This enables us to tran...

Embedding of Klein-Gordon and Dirac particle onto Riemannian submanifold in higher dimensional Minkowski space is given by using Hamiltonian BRST formalism. Up to the ordering and quantum potential term induced by embedding, obtained K-G equation is the usual one in Riemannian space, instead, the obtained Dirac equation is essentially different from the usual well known form using vierbein. The...

The usual concept of shape invariance is discussed and one extension of this concept is suggested. Gedenshtein [1] defined the “shape invariant” potentials by the relationship V+(x; a0)− V−(x; a1) = W (x, a0) +W ′(x, a0)−W (x; a1) +W ′(x; a1) = R(a1) (1) where W (x; a) is the superpotential, a0 and a1 stand for parameters of the supersymmetric partner potentials V+ and V−, R(a) is a constant. T...

the entanglement between a ?-type three-level atom and its spontaneous emission fields is investigated. the effect of spontaneously generated coherence (sgc) on entanglement between the atom and its spontaneous emission fields is then discussed. we find that in the presence of sgc the entanglement between the atom and its spontaneous emission fields is completely phase dependent, while in absen...

Theoretically, in order to describe the behavior of a spectrum, a mathematical model whichcould predict the spectrum characteristics is needed. Since in this study a Two-state system has beenused like models which was introduced previously past and could couple with the environment, theformer ideas have been extended in this study. we use the second quantized version for writing thisHamiltonian...

We examine the quantisation of a collective Hamiltonian for the two-baryon system derived by us in a previous paper. We show that by increasing the sophistication of the approximations we can obtain a bound state or a resonance not too far removed from the threshold with the quantum numbers of the deuteron. The energy of this state is shown to depend very sensitively on the parameters of the mo...