The quantum cylindrical quadrupole is a solution to the Schrödinger equation, i ℏ ℏ ∂ ∂ ∂ ∂ t ψ ψ ( x , t ) = − − ℏ ℏ 2 2 m ∂ ∂ 2 ∂ ∂ x 2 ψ ψ ( x , t ) + V ( x ) ψ ψ ( x , t ) , where ℏ ℏ is the reduced Planck constant, m is the mass of the particle, i is the imaginary unit and t is time.