Exam3_Example

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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online