Departmental Seminar

Analytical structure of the exact wave function of three particle systems

Professor Henryk A. Witek
Department of Applied Chemistry and Institute of Molecular Science,
National Chiao Tung University, Taiwan

Implicit analytical form of the ground state wave function for a three particle system [...] was proposed by Fock in 1954. Explicit determination of the angular Fock coefficients 𝑓𝑛𝑝(𝛼,𝜃) turned out to be a complex task; only few of them are found up to date. The Fock series can be considered as an extended Taylor series of the exact wave function in the coordinates [...] around the triple coalescence point 𝑟=0. The current talk will show how the Fock series emerges. In particular, it will show how the logarithmic terms appear in low-order Fock coefficients in order to guarantee physical behavior (continuity and finiteness) of the resulting wave function. We will address also the question of Fock expansion for helium in states with non-zero angular momentum and for helium without the Born-Oppenheimer approximation.

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