|標題:||Schrodinger equations with power potentials|
Witek, Henryk A.
Department of Applied Chemistry
Institute of Molecular science
|關鍵字:||Schrodinger equation;quasi-exactly solvable model;recurrence relation;Hessenberg determinant|
|摘要:||General formulae for solutions of the Schrodinger equation with power potentials are derived. The wavefunctions are expressed as products of the asymptotic factors and special forms of the Hessenberg determinants, in general, of infinite order. Conditions under which the order of the determinants becomes finite are determined. It is shown that solutions represented by the finite-order determinants may exist only if the highest power of the radial variable in the potential function is even. [GRAPHICS] .|