Monte Carlo Solutions of Schrödinger’s Equation for H₂⁺ Ion in Strong Magnetic Fields

抄録

The analytical expressions suitable for the Monte Carlo calculation to obtain the solution of Schrödinger’s equation of hydrogen molecular ion in a strong magnetic field are derived. The wave functions, the energy values and the equilibrium internuclear distances of 1σ_g state of H₂⁺ are obtained numericallly through the Monte Carlo simulation and compared with other results based on the variational method. The agreement between them is fairly good over a wide range of magnetic field.
The calculation of the energy values of 1π_g state of H₂⁺ for various internuclear distances taking a constant magnetic field as a parameter, shows that the antibonding 1π_g state in the absence of the external magnetic field changes to a bonding state with an increasing magnetic field. The lowest energy values and the equilibrium internuclear distances of 1π_g state are also calculated for various magnetic field.