Related papers: Exactly solvable associated Lame potentials and su…
We show how recent exact results in supersymmetric theories can be extended to models which include {\it explicit} soft supersymmetry breaking terms. We thus derive new exact results for non-supersymmetric models.
We show how the renormalizable see-saw mechanism in the context of supersymmetry and spontaneously broken B-L symmetry implies exact R-parity at all energies. We argue that supersymmetry plays an important role in providing a "canonical"…
We revisit the results on admissible transformations between normal linear systems of second-order ordinary differential equations with an arbitrary number of dependent variables under several appropriate gauges of the arbitrary elements…
We extend the notion of Dirac oscillator in two dimensions, to construct a set of potentials. These potentials becomes exactly and quasi-exactly solvable potentials of non-relativistic quantum mechanics when they are transformed into a…
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 propose a new approach based on the algebraization of the Associated Lam\'{e} equation \[-\psi''(x) + [ m(m+1)k^{2}sn^{2}x + \ell(\ell+1)k^{2}(cn^{2}x/dn^{2}x)]\psi(x) = E\psi(x)\] within sl(2,R) to derive the corresponding periodic…
Using first and second order supersymmetry formalism we obtain a class of exactly solvable potentials subject to moving boundary conditions.
Supersymmetric gauge theories in four dimensions can display interesting non-perturbative phenomena. Although the superpotential dynamically generated by these phenomena can be highly nontrivial, it can often be exactly determined. We…
Using the algebraic approach Lie symmetries of time dependent Schroedinger equations for charged particles interacting with superpositions of scalar and vector potentials are classified. Namely, all the inequivalent equations admitting…
One-dimensional superlattices with periodic spatial modulations of onsite potentials or tunneling coefficients can exhibit a variety of properties associated with topology or symmetry. Recent developments of ring-shaped optical lattices…
We consider quasinormal modes with complex energies from the point of view of the theory of quasi-exactly solvable (QES) models. We demonstrate that it is possible to find new potentials which admit exactly solvable or QES quasinormal modes…
In many applications to finite Fermi-systems, the pairing problem has to be treated exactly. We suggest a numerical method of exact solution based on SU(2) quasispin algebras and demonstrate its simplicity and practicality. We show that the…
We consider some examples of quantum super-integrable systems and the associated nonlinear extensions of Lie algebras. The intimate relationship between super-integrability and exact solvability is illustrated. Eigenfunctions are…
In this work it is shown how to obtain, in a simple way, localized (non- diffractive) subluminal pulses as exact analytic solutions to the wave equations. These new ideal subluminal solutions, which propagate without distortion in any…
The relaxed and unrelaxed formation energies of neutral antisites and interstitial defects in InP are calculated using ab initio density functional theory and simple cubic supercells of up to 512 atoms. The finite size errors in the…
Some exact solutions to the hypermultiplet low-energy effective action in N=2 supersymmetric four-dimensional gauge field theories with massive `quark' hypermultiplets are discussed. The need for a spontaneous N=2 supersymmetry breaking is…
PT symmetric complex potential V(r) = - r^4 + i a r^3 + b r^2 + i c r + i d/r + e/r^2 is studied. Arbitrarily large multiplets of its closed bound-state solutions with real energies are shown obtainable quasi-exactly (i.e., with a certain…
A series of exactly solvable non-trivial complex potentials (possessing real spectra) are generated by applying the Darboux transformation to the excited eigenstates of a non-Hermitian potential V(x). This method yields an infinite number…
A transformation method is applied to the second order ordinary differential equation satisfied by orthogonal polynomials to construct a family of exactly solvable quantum systems in any arbitrary dimensional space. Using the properties of…
A general method for solving linear differential equations of arbitrary order, is used to arrive at new representations for the solutions of the known differential equations, both without and with a source term. A new quasi-solvable…