Progress in analytical solution of Schrödinger equation for helium atom
Henryk Witek
National Chiao Tung University
Henryk Witek obtained MS degree from Jagiellonian University (Kraków, Poland, 1996) and PhD degree from Tokyo University (Japan, 2002) in the field of quantum chemistry. After a postdoctoral fellowship at Emory University (Atlanta, US, 20032005), he joined National Chiao Tung University (Hsinchu, Taiwan), where he currently holds full professor position (since 2011). His main interest is the exact solutions of quantum mechanical problems. He authored around 80 scientific publications, which received around 1700 citations. His hindex is 24. He is a recipient of 2014 Pople Medal and 2015 CMOA Promising Scientist Prize.
Abstract
In my talk I review the progress in the process of analytical solution of Schrödinger equation for the helium atom. The problems of two correlated electrons in a central field of nucleus, the simplest unsolved problem of... [ view full abstract ]
In my talk I review the progress in the process of analytical solution of Schrödinger equation for the helium atom. The problems of two correlated electrons in a central field of nucleus, the simplest unsolved problem of quantum mechanics, attracted a lot of attention over the last 80 years. Most of these results are almost completely unknown in the quantum community. Implicit analytical form of the ground state wave function for helium was proposed by Fock in 1954 [1]. Explicit determination of the angular Fock coefficients turned out to be a complex task; only few of them are found up to date [1–3]. The Fock series can be considered as an extended Taylor series of the exact wave function around the triple coalescence point. It is important to stress that the Fock series represents all the L=0 solutions to the Schrödinger equation, including the divergent ones. The identification of the physically meaningful solutions proceeds via studying the behavior of the Fock series in the limit of large electronnucleus separations. The current talk will show how the Fock series naturally emerges from a homogeneity expansion proposed by Hylleraas and further developed by our group. In particular, it will show how the logarithmic terms appear in loworder 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 nonzero angular momentum.
Authors

Henryk Witek
(National Chiao Tung University)
Topic Areas
Quantum simulation , Fundamental science for quantum technologies
Session
OS2bR236 » Fundamental science for quantum technologies (16:50  Thursday, 6th September, Room 236)
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