Therefore, − − d 2 d q 2 + q 2 = ( − − d d q + q ) ( d d q + q ) + 1 and the Schrödinger equation for the oscillator becomes, with substitution of the above and rearrangement of the factor of 1/2, ℏ ℏ ω ω [ 1 2 ( − − d d q + q ) 1 2 ( d d q + q ) + 1 2 ] ψ ψ ( q ) = E ψ ψ ( q ) .