Using that e i p j a is the translation operator, so that e i p j a ψ ψ ( x , y ) = ψ ψ ( x + a , y ) , where j = x , y , z and ψ ψ ( r ) = ψ ψ ( x , y ) is the particle's two-dimensional wave function. One can use W ( p − − q A ) as an effective Hamiltonian to obtain the following time-independent Schrödinger equation: