The Hamiltonian H specifies the energy levels and time evolution of a quantum theory. A
standard axiom of quantum mechanics requires that H be Hermitian because Hermiticity …

Abstract Quasi-Exactly Solvable Schrödinger Equations occupy an intermediate place
between exactly-solvable (eg the harmonic oscillator and Coulomb problems, etc.) and non …

Exactly solvable models, that is, models with explicitly and completely diagonalizable
Hamiltonians are too few in number and insufficiently diverse to meet the requirements of …

A new two-parameter family of quasi-exactly solvable quartic polynomial potentials is
introduced. Heretofore, it was believed that the lowest-degree one-dimensional quasi …

An infinite family of exactly solvable and integrable potentials on a plane is introduced. It is
shown that all already known rational potentials with the above properties allowing …

The main object of the present paper is to investigate the Dirac equation (Dirac fermions) in
presence of scalar and vector potential in a class of flat Gödel-type space-time called Som …

It is shown that all four superintegrable quantum systems on the Euclidean plane possess
the same underlying hidden algebra $ sl (3) $. The gauge-rotated Hamiltonians, as well as …

We discuss various questions that emerge in connection with the Lie-algebraic deformation
of the CP 1 sigma model in two dimensions. First, we supersymmetrize the original model …

This paper shows that there is a correspondence between quasi‐exactly solvable models in
quantum mechanics and sets of orthogonal polynomials {P n}. The quantum‐mechanical …

For almost two decades Prof. Shifman, a clear and pedagogical expositor, has been giving
review lectures on frontier topics in theoretical high energy physics. This two-volume book is …