yyrcd

2019

Nov 06

Hartree fork of H2 using gaussian type orbital

- Restricted Hartree-Fock SCF Calculations Using Microsoft Excel - could Demonstrate Variational Principle
- NZ Nano: Simple Quantum Chemistry: Hartree-Fock in Python
- Practical Introduction to Hartree-Fock Algorithm using Python
- modern-quantum-chemistry.pdf - BOOK p171
- www.physics.rutgers.edu/~haule/509/src_HF/Python/H2.py

Basis set: Basis Set Exchange (BSE)

Others:

- Evaluating the Overlap Integral (Optional) - Chemistry LibreTexts - Using elliptic coordinate
- GTOvsSTO

2019

Nov 03

- python - Understanding NumPy's einsum - Stack Overflow
- A basic introduction to NumPy's einsum – ajcr – Haphazard investigations
- 能「看到」的张量运算：因子图可视化

```
A = np.array([0, 1, 2])
B = np.array([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
(np.expand_dims(A, 1) * B).sum(axis=1) # array([ 0, 22, 76])
```

```
np.einsum('i,ij->ij', A, B) # array([[ 0, 0, 0, 0],
# [ 4, 5, 6, 7],
# [16, 18, 20, 22]])
np.einsum('i,ij->i', A, B) # array([ 0, 22, 76])
np.einsum('i,ij->', A, B) # 98
```

Here is what happens next:

A has one axis; we've labelled it

`i`

. And B has two axes; we've labelled axis 0 as`i`

and axis 1 as`j`

.By

the label`repeating`

`i`

in both input arrays, we are telling einsum that these two axes should betogether.`multiplied`

Notice that

`j`

does not appear as a label in our desired output. Bythe label, we're telling einsum to`omitting`

along this axis.`sum`

2019

Sep 30

(AB)

^{†}= B^{†}A^{†}Hermitian

Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own`conjugate transpose`

- Commutator
- If two operators commute

The observables A and B can be measured simultaneously with infinite precision - If the operators do not commute

They can't be prepared simultaneously to arbitrary precision, and there is an uncertainty relation between the observables

- If two operators commute