## Pg 254, Eqn 9.62


```python
from sympy import integrate, diff, symbols, exp, pi, solve
```


```python
xi, Z, a0, epsilon0, e = symbols('xi Z a0 epsilon0 e', real=True, positive=True)
```


```python
variational = (xi**2 - 2*Z*xi + (5/8)*xi) * ((e**2) / (4*pi*epsilon0*a0))
variational
```




$\displaystyle \frac{e^{2} \left(- 2 Z \xi + \xi^{2} + 0.625 \xi\right)}{4 \pi a_{0} \epsilon_{0}}$




```python
deriv_variational = diff(variational, xi)
deriv_variational
```




$\displaystyle \frac{e^{2} \left(- 2 Z + 2 \xi + 0.625\right)}{4 \pi a_{0} \epsilon_{0}}$




```python
solve(deriv_variational, xi)
```




    [Z - 0.3125]




```python

```

66eecf8c81406eb8d6e1e60daed8c9a7412f5ceb
ipynb
Jupyter Notebook
notebooks/variational_He_pg254.ipynb
akey7/basic-quantum-models
b2f7edd2fdd15b6f85ee3708f8c2dae24686fd07
BSD-2-Clause
notebooks/variational_He_pg254.ipynb
akey7/basic-quantum-models
b2f7edd2fdd15b6f85ee3708f8c2dae24686fd07
BSD-2-Clause
2021-07-12T15:49:00.000Z
2021-07-12T15:54:55.000Z
notebooks/variational_He_pg254.ipynb
akey7/basic-quantum-models
b2f7edd2fdd15b6f85ee3708f8c2dae24686fd07
BSD-2-Clause
Qwen/Qwen-72B
1. YES
2. YES