Calculation of Ground State Energy of Helium using Hylleraas Trial Function Expansion

Energy calculation of helium ground state has been done using the variational method. In this study the trial wave function of helium has been proposed which has included non linear parameters α and β. This wave function is a modification of the Hylleraas trial function. The trial wave function of helium is used to calculate helium ground state energy by varying the l > n > m series so that the number of terms is 12, 15, 18, 20, 24, 30, 36, 40, 48 terms.By using the Powell method to perform functional minimization of the expectation value equation, the minimum energy obtained is the helium ground state energy whcih is -2.901501710650829 a.u. The value of variational parameters from the results of optimization is also obtained, which is non linear parameters α and β.