solns21b-ps2-Jan11

solns21b-ps2-Jan11 - Chemistry 21b Problem set # 2 Out: 12...

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

View Full Document Right Arrow Icon

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

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

Unformatted text preview: Chemistry 21b Problem set # 2 Out: 12 January 2011 Due: 19 January 2011 Problems are worth: 1=25; 2=30; 3=20; 4=25. 1. Problem 10-17 McQuarrie, page 551, which shows that the simplest wavefunction for H + 2 , + = 1 / radicalbig 2(1 + S )(1 s A + 1 s B ), does not even qualitatively satisfy the virial theorem. 2. A somewhat extended version of problem 10-20 McQuarrie, pp. 551-552, about what is called the Scaling Theorem within the Born-Oppenheimer approximation. Start, as the text suggests, by deriving formulae for < T > and < V > when all of the coordinates are multiplied, or scaled, by a constant parameter . Heres the point. Now take the the results you get, namely < T > and < V > for arbitrary in terms of < T > | =1 and < V > | =1 , and write the expression for the total energy E . Treat as a variational parameter and find the optimal value of . From this, calculate the values of E, < T >, and < V > at opt . Show, from the numerical results in example 10-3, that this procedure for H + 2 directly yields an optimal opt = 1 . 238 and the energy listed in Table 10.2. Show also that the virial theorem is satisfied at this value of , without having to work through equations (10.31-10.32).through equations (10....
View Full Document

This note was uploaded on 01/03/2012 for the course CH 21b taught by Professor List during the Fall '10 term at Caltech.

Page1 / 10

solns21b-ps2-Jan11 - Chemistry 21b Problem set # 2 Out: 12...

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