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Unformatted text preview: 1 / 2 Z ∞∞ x 2 eγx 2 dx = ¯ h 2 γ 4 μ + k 4 γ ≥ E o Now, allow γ to vary and optimize E var : dE var dγ = ¯ h 2 4 μk 4 γ 2 = 0 γ = ( kμ ) 1 / 2 ¯ h ≡ α This leads, with no surprise, to the exact solutions to the 1D H.O. χ = ψ o ( x ) = ± α π ² 1 / 4 eαx 2 / 2 → E var = ¯ hω 2 = E o 2 2 Problem 2 What is the general expression for the Frst order perturbation correction to the ground state energy of a system with perturbation Hamiltonian ˆ H 1 ? 2.1 Solution E 1 o = Z all space ψ * ˆ H 1 ψ d 3 r 3 Problem 3 What are the e±ective nuclear charges ”seen” by electrons in the 1 s , 2 s , and 2 p atomic orbitals for the carbon atom? What is the true nuclear charge for this system? 3.1 Solution 1s = 5.67 2s = 3.22 2p = 3.14 3...
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This note was uploaded on 02/02/2012 for the course CHEM 444 taught by Professor Dybowski,c during the Fall '08 term at University of Delaware.
 Fall '08
 Dybowski,C
 Physical chemistry, Atom, pH

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