After any measurement aiming to detect the particle within the subset B, the wave function collapses to either μ μ X ( B ) ψ ψ ‖ ‖ μ μ X ( B ) ψ ψ ‖ ‖ = χ χ B ψ ψ ‖ ‖ χ χ B ψ ψ ‖ ‖ or ( 1 − − χ χ B ) ψ ψ ‖ ‖ ( 1 − − χ χ B ) ψ ψ ‖ ‖ , where ‖ ‖ ⋅ ⋅ ‖ ‖ is the Hilbert space norm on L 2 ( R , C ) .