Exam3_Example

# Exam3_Example - Exam III Example Problems 1 If is a guess...

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Exam III Example Problems 1. If Φ is a guess wave function, H is the Hamiltonian, and E 0 is the ground-state energy, which of the following is/are always true as a consequence of the variational principle? (a) Φ * H Φ d r E 0 (e) Φ * H Φ d r Φ * Φ d r > E 0 (b) Φ H Φ E 0 Φ Φ (f) (a) and (b) (c) The expectation value of H over Φ will be less than E 0 (g) (a) and (e) (d) The expectation value of H over Φ will be greater than E 0 + 1/2 a.u. (h) (a), (b), and (e) 2. What is < 1/ r > in a.u. for the one-electron wave function ψ 1 s r , θ , φ ; α ( ) = e r ? (a) 0 (e) 4 π / (2 α ) 2 (b) 1/2 (f) α (c) 1 (g) 2 α (d) π / α (h) None of the above (A useful formula: xe ax dx 0 = 1 a 2 ) 3. Which of the below statements is/are true? (a) Fermions have integer spin (e) Ψ = a (1) b (2) – b (1) a

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Exam3_Example - Exam III Example Problems 1 If is a guess...

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