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a) Briefly explain the meaning of $\bgroup\color{col1}$ \varepsilon$\egroup$ and $\bgroup\color{col1}$ T_c$\egroup$ .

b) Calculate the eigenvalues of $\bgroup\color{col1}$ {\mathcal H}_{\rm TLS}$\egroup$ .

c) Calculate the eigenvectors for the case $\bgroup\color{col1}$ \varepsilon=0$\egroup$ .

d) Use first order degenerate perturbation theory to calculate eigenvalues and eigenvectors of $\bgroup\color{col1}$ {\mathcal H}_{\rm TLS}$\egroup$ . Compare to the exact result

Tobias Brandes 2005-04-26