Another application of the ladder operator concept is found in the quantum mechanical treatment of the electronic energy of hydrogen-like atoms and ions. The Laplace–Runge–Lenz vector commutes with the Hamiltonian for an inverse square spherically symmetric potential and can be used to determine ladder operators for this potential. We can define the lowering and raising operators (based on the classical Laplace–Runge–Lenz vector) A → → = ( 1 Z e 2 μ μ ) { L → → × × p → → − − i ℏ ℏ p → → } + r → → r , where L → → is the angular momentum, p → → is the linear momentum, μ μ is the reduced mass of the system, e is the electronic charge, and Z is the atomic number of the nucleus. Analogous to the angular momentum ladder operators, one has A + = A x + i A y and A − − = A x − − i A y .