Exam_3abc_key

Exam_3abc_key - A,B,C 1. If is a guess wave function that...

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

View Full Document Right Arrow Icon
A,B,C NAME: ________________________________________________________________ 1. If Φ is a guess wave function that may or may not be normalized, 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) ! " * H ! d r ! " * ! d r # E 0 (c) H Φ = E Φ (b) " H " # E 0 (d) all of the above 2. What is the Born-Oppenheimer approximation? (a) Ignoring spin-orbit coupling in the Hamiltonian (c) Assuming that spin can be included in an ad hoc fashion (b) Assuming identical quantum mechanical particles to be indistinguishable from one another (d) Assuming nuclear and electronic motions to be decoupled so that electronic energies can be computed for fixed nuclear positions 3. For a particle in a box of length 1, which of the following trial wave functions would be likely to yield the best approximation to the exact ground state wave function ! 1 x ( ) = 2 sin " x ( ) 0 # x # 1 (assume all functions will be normalized) (a) ! x ( ) = x 1 " x ( ) (c) ! x ; a , b , c ( ) = cos a bx c ( ) , a , b , and c variational parameters (b) ! x ; a , b ( ) = x a 1 " x b ( ) , a and b variational parameters (d) ! x ; a ( ) = x a 1 " x ( ) , a a variational parameter
Background image of page 1

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

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

Page1 / 5

Exam_3abc_key - A,B,C 1. If is a guess wave function that...

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