这是一份bath巴斯大学PH10001作业代写的成功案

$$
E_{k}^{1} \equiv \bar{V}{k k}, $$ and $$ \psi{k}^{1}=-\sum_{j \neq{k}} \frac{\psi_{j}^{0}}{E_{k}^{0}-E_{j}^{0}} V_{j k}
$$
Here, ${k}$ denotes the modified degenerate states.
The second order correction is obtained by solving Eq. (59),
$$
\psi_{k}^{2}=-\frac{1}{E_{k}^{0}-H_{0}}\left(E_{k}^{0} \psi_{k}^{0}-V \psi_{k}^{1}\right)
$$

PH10001 COURSE NOTES ：

$$
\Psi=\sum_{l} C_{l} \Phi_{l}
$$
The individual “configuration” Slater determinants, $\Phi_{l}$, are constructed from spin-orbitals, $\phi_{j}$, given by
$$
\phi_{j}=|\alpha\rangle \sum_{\lambda} C_{\lambda j} \chi_{\lambda} \text { or }|\beta\rangle \sum_{\lambda} C_{\lambda j} \chi_{\lambda} \text {, }
$$
where $\chi_{\lambda}$ is a spatial basis function. The $\chi_{\lambda}$ generally fall into two classes:

• Slater-type orbitals (STOs)
  $$
  \chi_{\lambda}=N_{n l m \zeta} Y_{l m}(\theta, \phi) r^{n-1} \exp (-\zeta r),
  $$