Mathematical properties of generalized Sturmian functions

摘要: We study some mathematical properties of generalized Sturmian functions which are solutions a Schr¨ odinger-like equation supplemented by two boundary conditions. These functions, for any value the energy, defined in terms magnitude potential. One conditions is imposed at origin coordinate, where regularity required. The second point large distances. For negative energies, boundlike imposed. positive or complex incoming outgoing to deal with scattering problems; this case, since complex, themselves complex. Since all solve Sturm–Liouville problem, they allow us construct basis set must be orthogonal and complete: case even when Here we associated Hulth´ en potential, particular, spatial organization their nodes, demonstrate explicitly orthogonality. also show that overlap matrix elements, generally required bound state calculations, well defined. Many these expressed uncommon multivariable hypergeometric functions. Finally, applications particle Yukawa potential serve as