相关论文: Systematic Search of Exactly Solvable Non-Central …

Over the last decade, non-relativistic theories have attracted considerable attention. In general, such theories can be obtained by contracting relativistic parent theories. In this work, we discuss features of non-relativistic…

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…

We briefly summarize some recent theoretical developments in perturbative QCD, emphasizing new ideas which have led to widening the domain of applicability of perturbation theory. In particular, it is now possible to calculate efficiently…

After setting up a general model for supersymmetric classical mechanics in more than one dimension we describe systems with centrally symmetric potentials and their Poisson algebra. We then apply this information to the investigation and…

Extensions of nuclear supersymmetry are discussed, together with a proposal for new, more stringent and precise tests that probe the susy classification and specific two-particle correlations among supersymmetric partners. The combination…

The recently proposed PT-symmetric quantum mechanics works with complex potentials which possess, roughly speaking, a symmetric real part and an anti-symmetric imaginary part. We propose and describe a new exactly solvable model of this…

The theory of symmetric-hyperbolic systems is useful for constructing smooth solutions of nonlinear wave equations, and for studying their singularities, including shock waves. We present the main techniques which are required to apply the…

After an introduction to the Hierarchy Problem and to Supersymmetry we discuss the phenomenology of a motivated non-standard pattern of sparticle masses in the context of extensions of the Minimal Supersymmetric Standard Model.

We present a unified approach for solving and classifying exactly solvable potentials. Our unified approach encompasses many well-known exactly solvable potentials. Moreover, the new approach can be used to search systematically for a new…

Representation theory is shown to be incomplete in terms of enumerating all integrable limits of quantum systems. As a consequence, one can find exactly solvable Hamiltonians which have apparently strongly broken symmetry. The number of…

We consider supersymmetric quantum mechanical models with both local and nonlocal potentials. We present a nonlocal deformation of exactly solvable local models. Its energy eigenfunctions and eigenvalues are determined exactly. We observe…

The supersymmetric approach in the form of second order intertwining relations is used to prove the exact solvability of two-dimensional Schrodinger equation with generalized two-dimensional Morse potential for $a_0=-1/2$. This…

This theoretical review is intended to give non-theorists a flavor of the ideas driving the current efforts to experimentally find supersymmetry. We discuss the main reasons behind the expectation that supersymmetry may be "just around the…

Using supersymmetric quantum mechanics we develop a new method for constructing quasi-exactly solvable (QES) potentials with two known eigenstates. This method is extended for constructing conditionally-exactly solvable potentials (CES).…

The characteristic anti-linear (parity/time reversal, PT) symmetry of non-Hermitian Hamiltonians with real energies is presented as a source of two new forms of solvability of Schr\"{o}dinger's bound-state problems. In detail we describe…

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…

We study the perturbation by a critical term and a $(p-1)$-superlinear subcritical nonlinearity of a quasilinear elliptic equation containing a singular potential. By means of variational arguments and a version of the…

The supersymmetric theory of (color)superconductivity is investigated.

The difficulties of perturbation theory associated with unstable fundamental fields (such as the lack of exact gauge invariance in each order) are cured if one constructs perturbative expansion directly for probabilities interpreted as…

The classical theory of symmetric functions has a central position in algebraic combinatorics, bridging aspects of representation theory, combinatorics, and enumerative geometry. More recently, this theory has been fruitfully extended to…