Speaker
Description
The quantum problem of three bodies with Coulomb interaction is one of the most notable
nonintegrable problems in quantum mechanics. At the same time, extremely accurate numerical
solutions for the problem of bound states for a system of three particles may be obtained with modern
computers. For example, the nonrelativistic energy of the ground state of helium with a nucleus of an
infinite mass is now known accurately to 46 significant digits. In the present study, a version of the
variational method (the so called ”exponential” expansion) that allows to numerically solve the
quantum Coulomb three-body bound state problem with a very high precision, which is easily
applicable as well to the states with a nonzero angular momentum, is considered. This method is used
to calculate the nonrelativistic ionization energies of a helium atom for S, P, D, and F states. It is
shown that the developed method is an efficient and flexible instrument for studying Coulomb
systems. An analysis of convergence proves that the method is highly accurate and demonstrates that
nonrelativistic energies accurate up to 28-35 significant digits may be obtained with rather moderate
efforts. Calculations of the nonrelativistic ionization energy of the negative hydrogen ion H − are also
presented.
[1] C. Schwartz, Experiment and theory in computations of the He atom ground state. Int. J. Mod.
Phys.E 15, 877 (2006); C. Schwartz, Further Computations of the He atom ground state.
ArXiv:math-phys/0605018, (2006).
[2] V.I. Korobov, Nonrelativistic ionization energy for the helium ground state. Phys.Rev. A 66,
024501 (2002).
[3] V.I. Korobov, Coulomb three-body bound-state problem: variational calculations of nonrelatistic
energies. Phys. Rev.A. 61, 064503 (2000).
[4] Baker J.D., Phys.Rev.,A41,1247 (1990).
[5] Drake , et. all. Phys.Rev.,A65,054501 (2002).
[6]Frolov A.M., Phys.Rev.,E74,027702 (2006).
