(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Verify that acting on a state with winding m, the operator

[tex]e^{i\ell q_0/\~R}[/tex]

gives a state with winding [itex]m + \ell[/itex]

2. Relevant equations

Equation (17.83)

[tex]e^{-i\ell q_0/\~R}we^{i\ell q_0/\~R} = w + \frac{\ell}{\~R}[/tex]

3. The attempt at a solution

It seems easy: given |m> where w|m> = m|m> we have

[tex]w|e^{i\ell q_0/\~R}m> = e^{i\ell q_0/\~R}e^{-i\ell q_0/\~R}we^{i\ell q_0/\~R}|m> = e^{i\ell q_0/\~R}(w + \frac{\ell}{\~R})|m> = (m + \frac{\ell}{\~R})|e^{i\ell q_0/\~R}m>[/tex]

So is there a typo in the book?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Zwiebach QC 17.4, page 404

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**