Calculation of two dimensional helium atom ground state energy using variational methods with high precision calculation

One of the simplest system, where Schrödinger equation cannot be solved exactly, is atomic helium. However, extraordinarily powerful approximations, like variational methods are available to helium for high precision caluculations. In this study, two dimensional helium atom ground state energy using the variational method has been calculated to many significant digits. Overlap and hamiltonian matrix elements have been obtained analytically. A basis containing exponentials in all the interparticle distances have been used in calculation of these matrix elements. A new multiprecision program is written on Python with Mpmath which, is a pure - Python library for multiprecision floating-point arithmetic. The best ground state energy which have been obtained is -11.899 822 342 649 616 and this result is compatible with the results in literature.