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Lec2 (1) - 10.675 LECTURE 2 RICK RAJTER 1 Last Lecture...

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10.675 LECTURE 2 RICK RAJTER 1. Last Lecture Review Many Body PE surface. Schr¨ odinger’s Equation (SE) # Dimensions 2. Important Concepts Many Body PE surface. Schrodinger’s Equation. # Dimensions 3. Many Body SE 1 N 2 N M Z k 2 i + N N r� i vecr j r� i R k i i<j 1 H = i i j 3N - 6 Degrees of Freedom (DOF) in Non-Linear Case 3N - 5 DOF for linear. Each Molecule moves in the directions, hence 3N. In non-linear, substract 3 rotation and 3 translation (-6). In linear, substract 3 translation and 2 rotation (-5). 4. Today QM and Atomic Orbitals Permutation P ˆ i j and Pauli Principle Spin Orbitals Valence band theory and molecular 5. Born Oppenheimer approximation Theory that the electrons relax far faster than the protons. Thus, we can decouple nuclear-nuclear interaction terms from the electron terms. Date : Fall 2004. 1
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2 RICK RAJTER 6. Hydrogen Atom i ( r ) = E i φ i ( r ) H Hamiltonian φ i ”Atomic” orbital r position vector We can solve for the hydrogen wave function explicitly φ nlm ( r ) = ( φ, θ ) R nl Y l m NOTE: the solution neglects or doesn’t include the effects of spin.
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