A basis for variational calculations in
dimensions. (English) Zbl 1064.81023
Summary: We derive expressions for matrix elements for the Hamiltonian in dimensions. The basis functions in each angular momentum subspace are of the form . The matrix elements are given in terms of the gamma function for all . The significance of the parameters and and scale are discussed. Applications to a variety of potentials are presented, including potentials with singular repulsive terms of the form , perturbed Coulomb potentials , and potentials with weak repulsive terms, such as .
|81Q05||Closed and approximate solutions to quantum-mechanical equations|
|49S05||Variational principles of physics|