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Lecture+11+-+Quantum+mechanics

Lecture+11+-+Quantum+mechanics - Schrdinger Equation for...

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Schrödinger Equation for Hydrogen Atom H-atom has one electron and one proton. Proton fixed and electron can move in three dimensions (x, y, z). Potential energy (V) given by coulombic interaction: 0 ) ( 8 2 2 2 2 2 2 2 2 = + + + ψ π ψ ψ ψ V E h m z y x e (x) E (x) V dx (x) Ψ d m 8 π h n 2 n 2 2 2 n n Ψ = Ψ + r e Z V 0 2 2 4 πε = e - + r ) ( ) ( ˆ x E x H n n n Ψ = Ψ n=1,2,3 …
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Energy of H-atom is Quantized Principal quantum number n determines total energy of the electron: Same as Bohr Model for the case Z = 1. n = 1, 2, 3 … A e m h a e 529 . 0 2 2 0 0 = = π ε Bohr radius × = Δ 2 2 18 1 1 10 179 . 2 i f n n J E e - + 3 2 1 2 2 0 2 4 2 1 8 n h e m Z E e n ε = × × = = 2 18 2 0 0 2 1 10 179 . 2 1 8 n J n a e E n πε hcR H hcR H
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