Matrix elements

T⁽¹⁾Iₖ(p, k, bra, ket)

Compute the matrix elements of the pth component of the spherical tensor operator $T⁽¹⁾(Iₖ)$, which acts on the kth nucleus.

Note: in this function, Kronecker deltas are only enforced between the quantum numbers of the kth nucleus. The other quantum numbers are not required to match, because this tensor could be dotted with another operator, e.g., N ⋅ Iₖ, which allows mₙ to change.

Any Kronecker deltas on the remaining quantum numbers must be enforced where the dot product is eventually taken.

T⁽¹⁾N(p, bra, ket)

Compute the matrix elements of the pth component of the spherical tensor operator $T⁽¹⁾(N)$.

Note: in this function, Kronecker deltas are only enforced between the rotational quantum numbers. The nuclear quantum numbers are not required to match, because this tensor could be dotted with another operator, e.g., N ⋅ Iₖ, which allows mᵢ to change.

Any Kronecker deltas on the nuclear quantum numbers must be enforced where the dot product is eventually taken.

WignerJ1J(j, m)

Returns the same as WignerSymbols.wigner3j(j, 1, j, -m, 0, m), but computes it directly from the explicit formula.

WignerJ2J(j, m)

Returns the same as WignerSymbols.wigner3j(j, 2, j, -m, 0, m), but computes it directly from the explicit formula.

dipole_matrix_element(p::Int, bra::State, ket::State)::ComplexF64

nuclear_quadrupole(k::Int, bra::State, ket::State)::ComplexF64

nuclear_spin_rotation(k::Int, bra::State, ket::State)::ComplexF64

nuclear_spin_spin(bra::State, ket::State)::ComplexF64

rotation_matrix_element(bra::State, ket::State)::Float64

scalar_polarizability(bra::State, ket::State)

tensor_polarizability(p::Int, bra::State, ket::State)

zeeman_nuclear(k::Int, p::Int, bra::State, ket::State)::ComplexF64

zeeman_rotation(p::Int, bra::State, ket::State)::ComplexF64

δ(i, j)
δ(i::State, j::State)

Returns the Kronecker δ between i and j.

Uses ==(i,j) if possible. If i and j are both State, then this function computes the product of the Kronecker δs over all quantum numbers.