Bifurcations or related topics in two quantum systems are studied....[ Read more ]

Bifurcations or related topics in two quantum systems are studied.

The first system is a hydrogen ion in parallel electric and magnetic fields. I study cross section of electron detachment by a laser pulse. Effects of bifurcations of electronic periodic orbits on the cross section are demonstrated. We obtained a semiclassical and an approximate quantum-mechanical formula for the cross section. The results given by these theoretical formulas agree very well with numerical results of the exact quantum theory.

The second system I study is a hydrogen atom, also in parallel electric and magnetic fields. I study a numerical method for pure quantum-mechanical calculation of photoabsorption spectrum of the atom to a state near the ionization limit. In solving the Schrodinger equation directly, the Hamiltonian operator is represented by a matrix in terms of the so-called Sturmiam basis functions. The matrix is symmetric and sparse. The inverted and shifted method for solving eigenvalue problem of a matrix, and the Lonczos method for tridiagonalization of a matrix are employed.