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

Write out:

[tex]H_{SE}(\left|\right\beta,i_{\beta}\rangle\otimes\left|\right e_{j}\rangle)[/tex]

and

[tex]exp(-iH_{SE}t)(\left|\right\beta,i_{\beta}\rangle\otimes\left|\right e_{j}\rangle)[/tex]

Where:

[tex]H_{SE}=\sum_{\alpha,j}\gamma(\alpha,j)P^{(\alpha)}\otimes\left|e_{j}\right\rangle\left\langle e_{j}\right|[/tex]

and

[tex]P^{(\alpha)}=\sum_{i_{\alpha}}\left|i_{\alpha}\right\rangle\left\langle i_{\alpha}\right|[/tex]

([tex]\left|i_{\alpha}\right\rangle[/tex] can be written [tex]\left|\right\alpha,i_{\alpha}\rangle[/tex] where alpha is a quantum number indexed by [tex]i_{\alpha}[/tex] )

3. The attempt at a solution

For the first part I'm fairly sure it comes out as:

[tex]\sum_{\beta,j}\gamma(\beta,j)\left|\right\beta,i_{\beta}\rangle\otimes\left|\right e_{j}\rangle[/tex]

But the second part I am not sure of, is it something like:

[tex](Cos(t)-i\gamma(\alpha,j)Sin(t))(\left|\right\beta,i_{\beta}\rangle\otimes\left|\right e_{j}\rangle)[/tex]

Thanks!

**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: Interaction Hamiltonian

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