Schrodinger theory of the electronic structure of matter from a ‘Newtonian’ perspective

European Chemistry Congress

June 16-18, 2016 Rome, Italy

Viraht Sahni

City University of New York, USA

Posters & Accepted Abstracts: Chem Sci J

Abstract :

This talk is on a description of the Schr�¶dinger theory of the electronic structure of matter as defined by a system of N electrons in the presence of an arbitrary time-dependent external field Fext(rt) = â�� nabla v(rt), in terms of a â��Newtonianâ�� perspective. The perspective is based on the â��Quantal Newtonianâ�� second law of motion for each electron. This is a description in terms of â��classicalâ�� fields that pervade all space, and whose sources are quantal in that they are expectations of Hermitian operators taken with respect to the system wave function. In analogy to classical physics, there is then in addition to the external field, an internal field, and a field representative of the response of each electron. The internal field is a sum of fields representative of electron correlations due to the Pauli Exclusion Principle and Coulomb repulsion, the density, and kinetic effects. The perspective leads to an understanding of the intrinsic self-consistent nature of the Schr�¶dinger equation. On summing the law over all electrons, each component of the internal field vanishes (as is the case in classical physics), thereby leading to Ehrenfestâ��s theorem. The â��Quantal Newtonianâ�� first law, a special case, is in turn descriptive of stationary state Schr�¶dinger theory. The individual electron perspective will be explicated for both a ground and excited state via an exactly solvable interacting model system. This interpretation of Schr�¶dinger theory constitutes the basis for Quantal Density Functional Theory, and leads to insights into traditional Density Functional Theory and Quantum Fluid Dynamics. VSAHNI@brooklyn.cuny.edu