# HW7 - PHY4221 Quantum Mechanics(Fall Term Of 2004 Problem...

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Unformatted text preview: PHY4221 Quantum Mechanics (Fall Term Of 2004) Problem Set 7 (Answers) Question 1: The unperturbed eigen state and eigen energy are respectively: ( 29 ( 29 ( 29 3/ 2 , , 2 2 2 2 2 , , 2 2 sin sin sin 2 l m n l m n l x m y n z a a a a l m n E ma π π π ψ π = ÷ + + = h (1) The ground state without perturbation is described by: ( 29 ( 29 2 2 111 2 3/ 2 1,1,1 3 2 2 sin sin sin E ma x y z a a a a π π π π ψ = = ÷ h (2) When perturbation is added in, the first order correction of the ground state energy is given by: ( 29 1 1,1,1 1,1,1 1,1,1 3 2 2 2 3 2 2 2 2 2 2 3 sin sin sin 4 2 4 3 8 sin sin sin 4 2 4 2 a a a E H x y z a a a dx dy dz a V x y z a a a a V V ψ ψ π π π δ δ δ π π π ′ = =--- ÷ ÷ ÷ ÷ = = ∫ ∫ ∫ (3) The second order correction is given by: ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 , , 1,1,1 2 1,1,1 , , 1,1,1 1,1,1 , , 2 2 2 2 2 2 , ,...
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HW7 - PHY4221 Quantum Mechanics(Fall Term Of 2004 Problem...

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