Other utilities

Parity

AtomicLevels defines the Parity type, which is used to represent the parity of atomic states etc.

AtomicLevels.Parity — Type
struct Parity

Represents the parity of a quantum system, taking two possible values: even or odd.

The integer values that correspond to even and odd parity are +1 and -1, respectively. Base.convert can be used to convert integers into Parity values.

julia> convert(Parity, 1)
even

julia> convert(Parity, -1)
odd

The parity values also define an algebra and an ordering:

julia> p"odd" < p"even"
true

julia> p"even" * p"odd"
odd

julia> (p"odd")^3
odd

julia> -p"odd"
even

The exported parity function is overloaded for many of the types in AtomicLevels, defining a uniform API to determine the parity of an object.

JJ to LSJ

AtomicLevels.jj2lsj — Function
jj2lsj([T=Float64, ]orbs...)

Generates the block-diagonal matrix that transforms jj-coupled configurations to lsj-coupled ones.

The blocks correspond to invariant subspaces, which rotate among themselves to form new linear combinations.

They are sorted according to n,ℓ and within the blocks, the columns are sorted according to mⱼ,j (increasing) and the rows according to s,ℓ,m (increasing).

E.g. the p-block will have the following structure:

 ⟨p;-1,↓|3/2,-3/2⟩  │       ⋅                  ⋅             │       ⋅                ⋅           │       ⋅
 ───────────────────┼────────────────────────────────────────┼────────────────────────────────────┼─────────────────
      ⋅             │  ⟨p;0,↓|1/2,-1/2⟩   ⟨p;0,↓|3/2,-1/2⟩   │       ⋅                ⋅           │       ⋅
      ⋅             │  ⟨p;-1,↑|1/2,-1/2⟩  ⟨p;-1,↑|3/2,-1/2⟩  │       ⋅                ⋅           │       ⋅
 ───────────────────┼────────────────────────────────────────┼────────────────────────────────────┼─────────────────
      ⋅             │       ⋅                  ⋅             │  ⟨p;1,↓|1/2,1/2⟩  ⟨p;1,↓|3/2,1/2⟩  │       ⋅
      ⋅             │       ⋅                  ⋅             │  ⟨p;0,↑|1/2,1/2⟩  ⟨p;0,↑|3/2,1/2⟩  │       ⋅
 ───────────────────┼────────────────────────────────────────┼────────────────────────────────────┼─────────────────
      ⋅             │       ⋅                  ⋅             │       ⋅                ⋅           │  ⟨p;1,↑|3/2,3/2⟩

Index