```python
from sympy import pi, sqrt, erf, integrate, var, S, exp, init_printing, oo, Symbol
```


```python
var("r")
alpha = Symbol("alpha", positive=True)
```


```python
g = alpha**3/pi**(S(3)/2)*exp(-alpha**2*r**2)
```


```python
V = erf(alpha*r)/r
```


```python
Ig = 4*pi*integrate(g*(1/r-V)*r**2, (r, 0, oo))
```


```python
Isph = 4*pi*integrate((1/r-V)*r**2, (r, 0, 1))
```


```python
alpha_code = 37
```


```python
Ig.subs(alpha, sqrt(alpha_code)).n(25)
```




    2.010320207622576710962755




```python
Isph.subs(alpha, sqrt(alpha_code)).n(25)
```




    0.08490790955648089702710017




```python
e = V.subs(alpha, sqrt(alpha_code))
for i in range(1, 18):
    print i, e.subs(r, S(1)/10**i).n(25)
```

    1 6.103391218853852058466783
    2 6.855206721888216457088578
    3 6.863577866679608029294916
    4 6.863661671059414495539896
    5 6.863662509112513937641552
    6 6.863662517493045862208506
    7 6.863662517576851181547190
    8 6.863662517577689234740586
    9 6.863662517577697615272520
    10 6.863662517577697699077840
    11 6.863662517577697699915893
    12 6.863662517577697699924273
    13 6.863662517577697699924357
    14 6.863662517577697699924358
    15 6.863662517577697699924358
    16 6.863662517577697699924358
    17 6.863662517577697699924358



```python
print "Ig = %.22f_dp / rc" % Ig.subs(alpha, sqrt(alpha_code)).n(25)
print "Isph = %.22f_dp * rc**2" % Isph.subs(alpha, sqrt(alpha_code)).n(25)
print "v0 = %.22f_dp / rc" % e.subs(r, S(1)/10**18).n(25)
```

    Ig = 2.0103202076225765715378_dp / rc
    Isph = 0.0849079095564808927765_dp * rc**2
    v0 = 6.8636625175776977414444_dp / rc


cfd6bd473730206573006deea2e011622a8f8983
ipynb
Jupyter Notebook
src/tests/nb/Gaussian analytic.ipynb
certik/hfsolver
b4c50c1979fb7e468b1852b144ba756f5a51788d
BSD-2-Clause
2015-03-24T13:06:39.000Z
2022-03-29T00:14:02.000Z
src/tests/nb/Gaussian analytic.ipynb
certik/hfsolver
b4c50c1979fb7e468b1852b144ba756f5a51788d
BSD-2-Clause
2015-03-25T04:59:43.000Z
2017-06-06T23:00:09.000Z
src/tests/nb/Gaussian analytic.ipynb
certik/hfsolver
b4c50c1979fb7e468b1852b144ba756f5a51788d
BSD-2-Clause
2016-01-20T13:38:22.000Z
2020-11-24T15:35:43.000Z
Qwen/Qwen-72B
1. YES
2. YES