Sturm expansions in many-fermion problems

Kevin E. Schmidt, Malvin H. Kalos

Antonio S. de Castro

The problem of a fermion subject to a a scalar inversely linear potential in a two‐dimensional world is mapped into a Sturm‐Liouville problem for nonzero eigenenergies. This mapping gives rise to an effective Kratzer potential and exact bounded solutions are found in closed form. The normalizable zero‐eigenmode solution is also found. A few unusual results are revealed.

Kevin E. Schmidt, Malvin H. Kalos

S. I. Nikitin, A. I. Sherstyuk

Different variants of the generalized formulation of the eigenvalue problem related to a single-particle Schrödinger equation are considered. The nature of the spectrum of problems for a bundle of operators containing the Hamiltonian of the system is analyzed in relation to the form of the weighting operator. For rather general conditions, corresponding systems of eigenfunctions provide diagonal representations of the Green’s function and provide of a rather fast convergence of expansions over intermediate states. Cases of potentials with Coulomb asymptotics and short-range potentials are considered.

M. Moshińsky, H. Hernández-Saldaña, A. Suárez-Moreno

The Sturm-Coulomb problem is an integrable one since its symmetry group is O (4). When we apply to it a magnetic field, this symmetry is broken and reduced to the O (2) group. The problem is then nonintegrable, but we can derive its matrix representation in a basis in which the Sturm-Coulomb problem alone is diagonal. We use this matrix representation to obtain the corresponding eigenvalues and their nearest neighbor spacing distribution. From the histogram of the latter, we discuss the presence or absence of quantum chaos as a function of the intensity H of the magnetic field and the angular momentum m in the direction of this field.

Robert William Jones, Franz Mohling