M. Lieber

The Runge–Lenz vector for the two‐dimensional hydrogen atom

The recent discovery of novel properties possessed by two‐dimensional systems has led to the investigation of properties of the hydrogen atom in two dimensions. With proper definition of the system, the so‐called Runge–Lenz vector may be defined for this system, and shown to be related to the underlying O(3) symmetry, just as for the three‐dimensional system, although some interesting aspects are revealed.

The Coulomb Green’s function

It is something of a miracle that the nonrelativistic Schrodinger equation with a Coulomb potential can be solved for the wavefunction in exact analytic form. Even more miraculous is the result of Schwinger which enables the Green’s function to be solved in closed form, for this is in effect, an infinite sum of wavefunction products. In the relativistic case too the wavefunction can be found in closed form, but as yet no such result for the Green’s function has been found. This lecture provides a brief overview of the situation with an emphasis on the ‘‘hidden symmetry’’ which underlies the nonrelativisitic problem and its degenerate form which carries over to the relativistic case.

Thomas-forbidden particle capture

At high energies, in particle-capture processes between ions and atoms, classical kinematic requirements show that generally double-collision Thomas processes dominate. However, for certain mass-ratios these processes are kinematically forbidden. This paper explores the possibility of capture for such processes by triple or higher order collision processes.

Matrix analysis of classical elastic collisions

The velocities of two bodies before and after an elastic collision can be related by a matrix transformation in one and two dimensions. We demonstrate a very simple relation between the one- and two-dimensional collision matrices.