yyrcd

2019

Nov 06

Hartree fork of H2 using gaussian type orbital

Basis set: Basis Set Exchange (BSE)

Others:

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

2019

Nov 03

#### einsum

``````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 `repeating` the label `i` in both input arrays, we are telling einsum that these two axes should be `multiplied` together.

• Notice that `j` does not appear as a label in our desired output. By `omitting` the label, we're telling einsum to `sum` along this axis.

2019

Sep 30

• (AB) = BA

• 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 