Lecture17 - Simplification of the hydrogenatom problem By...

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1 Physical Chemistry Lecture 17 The Hydrogen Atom, a Central- Force Problem The hydrogen atom Consists of two particles, a positively charged nucleus and a negatively charged electron Hamiltonian has three terms Nuclear kinetic energy Electronic kinetic energy Nuclear-electron Coulombic potential energy | | 4 1 2 2 2 0 2 2 ne e e n n ne e n e m p m p V T T H r  Center of mass Hamiltonian as a function of nuclear and electronic co- ordinates is complex Define Center of mass, R CM Relative position, r Total mass, M Reduced mass, 2 2 2 2 2 2 2 2 2 1 2 1 2 1 2 1 2 1 1 2 2 2 1 1 p M P m p m p m m m m m m M M m M m CM CM r r r r r R Simplification of the hydrogen- atom problem By substitution, the hydrogen-atom Hamiltonian becomes Decompose into two problems rel CM CM H H r e p P M H 2 0 2 2 4 1 2 1 2 1 rel CM rel CM rel rel rel rel CM CM CM CM E E E E H E H
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This note was uploaded on 02/02/2012 for the course CHEM 419 taught by Professor Staff during the Fall '10 term at University of Delaware.

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Lecture17 - Simplification of the hydrogenatom problem By...

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