# fock_basis¶

edrixs.fock_basis.combination(n, m)[source]

Calculate the combination $$C_{n}^{m}$$,

$C_{n}^{m} = \frac{n!}{m!(n-m)!}.$
Parameters
n: int

Number n.

m: int

Number m.

Returns
res: int

The calculated result.

Examples

>>> import edrixs
>>> edrixs.combination(6, 2)
15

edrixs.fock_basis.fock_bin(n, k)[source]

Return all the possible $$n$$-length binary where $$k$$ of $$n$$ digitals are set to 1.

Parameters
n: int

Binary length $$n$$.

k: int

How many digitals are set to be 1.

Returns
res: list of int-lists

A list of list containing the binary digitals.

Examples

>>> import edrixs
>>> edrixs.fock_bin(4, 2)
[[1, 1, 0, 0],
[1, 0, 1, 0],
[1, 0, 0, 1],
[0, 1, 1, 0],
[0, 1, 0, 1],
[0, 0, 1, 1]]

edrixs.fock_basis.get_fock_basis_by_NJz(norb, N, jz_list)[source]

Get decimal digitals to represent Fock states, use good quantum number:

• total angular momentum $$J_{z}$$

Parameters
norb: int

Number of orbitals.

N: int

Number of total occupancy.

jz_list: list of int

Quantum number $$j_{z}$$ for each orbital.

Returns
res: dict

A dictionary containing the decimal digitals, the key is good quantum numbers $$j_{z}$$, the value is a list of int.

Examples

>>> import edrixs
>>> edrixs.get_fock_basis_by_NJz(6, 2, [-1, 1, -3, -1, 1, 3])
{
-6: [],
-5: [],
-4: [5, 12],
-3: [],
-2: [6, 9, 20],
-1: [],
0: [3, 10, 17, 36, 24],
1: [],
2: [18, 33, 40],
3: [],
4: [34, 48],
5: [],
6: []
}

edrixs.fock_basis.get_fock_basis_by_NLz(norb, N, lz_list)[source]

Get decimal digitals to represent Fock states, use good quantum number:

• orbital angular momentum $$L_{z}$$

Parameters
norb: int

Number of orbitals.

N: int

Number of total occupancy.

lz_list: list of int

Quantum number $$l_{z}$$ for each orbital.

Returns
res: dict

A dictionary containing the decimal digitals, the key is good quantum numbers $$L_{z}$$, the value is a list of int.

Examples

>>> import edrixs
>>> edrixs.get_fock_basis_by_NLz(6, 2, [-1, -1, 0, 0, 1, 1])
{
-2: [3],
-1: [5, 6, 9, 10],
0: [12, 17, 18, 33, 34],
1: [20, 36, 24, 40],
2: [48]
}

edrixs.fock_basis.get_fock_basis_by_NSz(norb, N, sz_list)[source]

Get decimal digitals to represent Fock states, use good quantum number:

• spin angular momentum $$S_{z}$$

Parameters
norb: int

Number of orbitals.

N: int

Number of total occupancy.

sz_list: list of int

Quantum number $$s_{z}$$ for each orbital.

Returns
res: dict

A dictionary containing the decimal digitals, the key is good quantum numbers $$S_{z}$$, the value is a list of int.

Examples

>>> import edrixs
>>> edrixs.get_fock_basis_by_NSz(6, 2, [1, -1, 1, -1, 1, -1])
{
-2: [10, 34, 40],
-1: [],
0: [3, 6, 9, 12, 18, 33, 36, 24, 48],
1: [],
2: [5, 17, 20]
}

edrixs.fock_basis.get_fock_basis_by_N_LzSz(norb, N, lz_list, sz_list)[source]

Get decimal digitals to represent Fock states, use good quantum number:

• orbital angular momentum $$L_{z}$$

• spin angular momentum $$S_{z}$$

Parameters
norb: int

Number of orbitals.

N: int

Number of total occupancy.

lz_list: list of int

Quantum number $$l_{z}$$ for each orbital.

sz_list: list of int

Quantum number $$s_{z}$$ for each orbital.

Returns
basis: dict

A dictionary containing the decimal digitals, the key is a tuple containing good quantum numbers ( $$l_{z}$$, $$s_{z}$$), the value is a list of int.

Examples

>>> import edrixs
>>> edrixs.get_fock_basis_by_N_LzSz(6, 2, [-1, -1, 0, 0, 1, 1], [1, -1, 1, -1, 1, -1])
{
(-2, -2): [],
(-2, -1): [],
(-2, 0): [3],
(-2, 1): [],
(-2, 2): [],
(-1, -2): [10],
(-1, -1): [],
(-1, 0): [6, 9],
(-1, 1): [],
(-1, 2): [5],
(0, -2): [34],
(0, -1): [],
(0, 0): [12, 18, 33],
(0, 1): [],
(0, 2): [17],
(1, -2): [40],
(1, -1): [],
(1, 0): [36, 24],
(1, 1): [],
(1, 2): [20],
(2, -2): [],
(2, -1): [],
(2, 0): [48],
(2, 1): [],
(2, 2): []
}

edrixs.fock_basis.get_fock_basis_by_N_abelian(norb, N, a_list)[source]

Get decimal digitals to represent Fock states, use some Abelian good quantum number.

Parameters
norb: int

Number of orbitals.

N: int

Number of total occupancy.

a_list: list of int

Quantum number of the Abelian symmetry for each orbital.

Returns
basis: dict

A dictionary containing the decimal digitals, the key is good quantum numbers, the value is a list of int.

edrixs.fock_basis.get_fock_bin_by_N(*args)[source]

Get binary form to represent a Fock state.

Parameters
args: ints

args[0]: number of orbitals for 1st-shell,

args[1]: number of occupancy for 1st-shell,

args[2]: number of orbitals for 2nd-shell,

args[3]: number of occupancy for 2nd-shell,

args[ $$2N-2$$]: number of orbitals for $$N$$ th-shell,

args[ $$2N-1$$]: number of occupancy for $$N$$ th-shell.

Returns
result: list of int list

The binary form of Fock states.

Examples

>>> import edrixs
>>> edrixs.get_fock_bin_by_N(4, 2)
[[1, 1, 0, 0],
[1, 0, 1, 0],
[1, 0, 0, 1],
[0, 1, 1, 0],
[0, 1, 0, 1],
[0, 0, 1, 1]]

>>> edrixs.get_fock_bin_by_N(4, 2, 2, 1)
[[1, 1, 0, 0, 1, 0],
[1, 0, 1, 0, 1, 0],
[1, 0, 0, 1, 1, 0],
[0, 1, 1, 0, 1, 0],
[0, 1, 0, 1, 1, 0],
[0, 0, 1, 1, 1, 0],
[1, 1, 0, 0, 0, 1],
[1, 0, 1, 0, 0, 1],
[1, 0, 0, 1, 0, 1],
[0, 1, 1, 0, 0, 1],
[0, 1, 0, 1, 0, 1],
[0, 0, 1, 1, 0, 1]]

edrixs.fock_basis.get_fock_full_N(norb, N)[source]

Get the decimal digitals to represent Fock states.

Parameters
norb: int

Number of orbitals.

N: int

Number of occupancy.

Returns
res: list of int

The decimal digitals to represent Fock states.

Examples

>>> import edrixs
>>> edrixs.fock_bin(4,2)
[[1, 1, 0, 0],
[1, 0, 1, 0],
[0, 1, 1, 0],
[1, 0, 0, 1],
[0, 1, 0, 1],
[0, 0, 1, 1]]

>>> import edrixs
>>> edrixs.get_fock_full_N(4,2)
[3, 5, 6, 9, 10, 12]

edrixs.fock_basis.write_fock_dec_by_N(N, r, fname='fock_i.in')[source]

Get decimal digitals to represent Fock states, sort them by ascending order and then write them to file.

Parameters
N: int

Number of orbitals.

r: int

Number of occuancy.

fname: string

File name.

Returns
ndim: int

The dimension of the Hilbert space

Examples

>>> import edrixs
>>> edrixs.write_fock_dec_by_N(4, 2, 'fock_i.in')
file fock_i.in looks like
15
3
5
6
9
10
12
17
18
20
24
33
34
36
40
48


where, the first line is the total numer of Fock states, and the following lines are the Fock states in decimal form.