Ladder Operators for Quantum Systems Confined by Dihedral Angles

We report the identification and construction of raising and lowering operators for the complete eigenfunctions of isotropic harmonic oscillators confined by dihedral angles, in circular cylindrical and spherical coordinates; as well as for the hydrogen atom in the same situation of confinement, in spherical, parabolic and prolate spheroidal coordinates. The actions of such operators on any eigenfunction are examined in the respective coordinates, illustrating the possibility of generating the complete bases of eigenfunctions in the respective coordinates for both physical systems. The relationships between the eigenfunctions in each pair of coordinates, and with the same eigenenergies are also illustrated

Green's function and stability of a linear partial difference scheme

AbstractThis paper is concerned with a linear partial difference equation which arises from discretizing a heat and a first order wave equations. A Green's function for this equation is derived. Various representation theorems, monotonicity, and oscillatory properties of the Green's functions are obtained. Then by means of the representation theorems, we derive several stability criteria for arbitrary solutions of this equation