In the past ten years, the ideas of supersymmetry have been profitably applied to many
nonrelativistic quantum mechanical problems. In particular, there is now a much deeper …

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 …

We discuss a new class of spectral problems discovered recently which occupies an
intermediate position between the exactly-solvable problems (like the famous harmonic …

We analyze bound modes of two-dimensional massless Dirac fermions confined within a
hyperbolic secant potential, which provides a good fit for potential profiles of existing top …

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 …

Recently developed methods to investigate quantum spin systems are reviewed. These
methods are based on somewhat unconventional applications of the spin coherent state …

We discuss a new class of spectral problems discovered recently which occupies an
intermediate position between the exactly-solvable problems (eg, harmonic oscillator) and …