p^~ congruent left bracketing bar ϕ_i(x)〉〈ϕ_i(t) right bracketing bar p^~ sum_j c_j left bracketing bar ϕ_j(t)〉 = c_i left bracketing bar ϕ_i(x)〉 sum_i left bracketing bar ϕ_i(x)〉〈ϕ_i(x) right bracketing bar = 1.

bra | ket | projection | projection matrix