Subspace

b = FockBasis(5)
b_sub = SubspaceBasis(b, [fockstate(b, 1), fockstate(b, 2)])

P = projector(b_sub, b)

x = coherentstate(b, 0.5)
x_prime = P*x
y = dagger(P)*x_prime # Not equal to x

Oftentimes it is possible to restrict a large Hilbert to a small subspace while still retaining the most important physical effects. This reduction can be done with the SubspaceBasis which is implemented as:

struct SubspaceBasis <: Basis
    shape::Vector{Int}
    superbasis::Basis
    basisstates::Vector{Ket}
end

Operators

To project states into the subspace or re-embed them into the super-space a projection operator can be used:

• projector

Additional functions

If the states used to define the subspace are not orthonormal one can use the orthonormalize function to obtain an ONB:

• QuantumOpticsBase.orthonormalize

Examples

• N-Particles in a double-well potential