```python
from sympy import *
init_printing() # For Sympy
from IPython.display import display
```

## Simple Pade form for the Jastrow factor.

The value of $A$ is fixed by the cusp condition at $r=0$.


```python
A, B, r = symbols('A B r')
u = A*r/(1.0 + B*r) - A/B
sym_u = Symbol('u')
display(Eq(sym_u,u))
```


```python
# Symbolic derivatives
du = diff(u, r)
du = simplify(du)
sym_du = Symbol('du')/Symbol('dr')
display(Eq(sym_du, du))
ddu = simplify(diff(u, r, 2))
sym_ddu = Symbol('d^2')*Symbol('u')/Symbol('dr^2')
display(Eq(sym_ddu, ddu))

```


```python
# Substitute concrete values to evaluate
vals = {A:-0.25, B: 0.1, r:1.0}
display(Eq(sym_u, u.subs(vals)))
display(Eq(sym_du, du.subs(vals)))
display(Eq(sym_ddu, ddu.subs(vals)))
```


```python

```

72a8ef31aa170a96d79a728d161bde6eb0110c9e
ipynb
Jupyter Notebook
Wavefunctions/Pade_Jastrow.ipynb
QMCPACK/qmc_algorithms
015fd1973e94f98662149418adc6b06dcd78946d
MIT
2018-02-06T06:15:19.000Z
2019-11-26T23:54:53.000Z
Wavefunctions/Pade_Jastrow.ipynb
chrinide/qmc_algorithms
015fd1973e94f98662149418adc6b06dcd78946d
MIT
2017-03-23T17:17:04.000Z
2017-03-23T17:17:04.000Z
Wavefunctions/Pade_Jastrow.ipynb
chrinide/qmc_algorithms
015fd1973e94f98662149418adc6b06dcd78946d
MIT
2017-11-14T20:25:00.000Z
2022-02-28T06:02:01.000Z
Qwen/Qwen-72B
1. YES
2. YES