This is a special case of shape invariance, discussed below. Taking without proof the introductory theorem mentioned above, it is apparent that the spectrum of H ( 1 ) will start with E 0 = 0 and continue upwards in steps of ℏ ℏ ω ω . The spectra of H ( 2 ) and H H O will have the same even spacing, but will be shifted up by amounts ℏ ℏ ω ω and ℏ ℏ ω ω / 2 , respectively. It follows that the spectrum of H H O is therefore the familiar E n H O = ℏ ℏ ω ω ( n + 1 / 2 ) .