We obtain upper bounds on the number of finite sets S \mathcal {S} <...

We comment that the conditionally exactly solvable potential of Dutt et al (1995 J. Phys. A: Math. Gen. 28 L107) and the exactly solvable potential from which it is derived form a dual system.

We investigate two methods of obtaining exactly solvable potentials with analytic forms. PACS numbers:03.65.Ge,11.30.Pb There are two methods of obtaining exactly solvable potentials in quantum mechanics. The first method was developed by applying the technique of supersymmetry (SUSY) to the Schrödinger equation and obtain two potentials with almost identical spectra. The two potentials can be ...

Criteria are given for determining whether an irreducible sextic equation with rational coefficients is algebraically solvable over the complex number field C.

The purpose of this paper is to present some new, simpler examples of recursively based undecidable varieties of finite type having solvable word problems.

We describe three di erent methods for generating quasi-exactly solvable potentials, for which a nite number of eigenstates are analytically known. The three methods are respectively based on (i) a polynomial ansatz for wave functions; (ii) point canonical transformations; (iii) supersymmetric quantum mechanics. The methods are rather general and give considerably richer results than those avai...