Toward Exact Analytical Wave Function of Helium Atom: Two Techniques for Constructing Homogeneous Functions of Kinetic Energy Operator

We discuss two general techniques for constructing homogeneous functions φ of the kinetic energy operator T for the helium atom in a state of symmetry S. The first technique is based on algebraic identification of the kernel of T in a space spanned by some predetermined set of basis functions. The second technique, analytic in nature, constructs the homogeneous functions of T as formal power series with coefficients deduced from recurrence relations stemming from the requirement Tφ=0. Both approaches are capable of producing a great variety of homogeneous functions φ with arbitrary homogeneity that can prove useful for constructing the exact ground state wave function for the helium atom.