Nonrelativistic ionization energy levels of a helium atom

Abstract

The nonrelativistic ionization energy levels of a helium atom are calculated for S, P, and D states. The calculations are based on the variational method of “exponential” expansion. Variational wave functions of bound states were obtained by solving the Schrodinger equation for the quantum three body problem with Coulomb interaction using a variational approach based on exponential expansion with the parameters of exponents being chosen in a pseudorandom way. The convergence of the calculated energy levels is studied as a function of the number of basis functions (N). This allows us to claim that the obtained energy values (including the values for the states with a nonzero angular momentum) are accurate to 20 significant digits.

Keywords

• Key words
• variational method
• expansion
• variational principle
• Schrӧdinger equation
• inverse iteration method. PACS numbers