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Toward Exact Analytical Wave Function of Helium Atom: Two Techniques for Constructing Homogeneous Functions of Kinetic Energy Operator
Author(s) -
BingHau He,
A. Witek Henryk
Publication year - 2016
Publication title -
journal of the chinese chemical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 45
eISSN - 2192-6549
pISSN - 0009-4536
DOI - 10.1002/jccs.201500086
Subject(s) - wave function , chemistry , helium atom , kinetic energy , homogeneous , operator (biology) , series (stratigraphy) , helium , atom (system on chip) , statistical physics , quantum mechanics , physics , paleontology , biochemistry , organic chemistry , repressor , biology , computer science , transcription factor , gene , embedded system
We discuss two general techniques for constructing homogeneous functions c 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 Tc =0. Both approaches are capable of producing a great variety of homogeneous functions c with arbitrary homogeneity that can prove useful for constructing the exact ground state wave function for the helium atom.