The Hamiltonian can also be written more simply by noting that the cyclotron frequency is ω c = qB / m, giving H ^ ^ = p ^ ^ x 2 2 m + 1 2 m ω ω c 2 ( x ^ ^ − − ℏ ℏ k y m ω ω c ) 2 + p ^ ^ z 2 2 m . This is exactly the Hamiltonian for the quantum harmonic oscillator, except with the minimum of the potential shifted in coordinate space by x 0 = ħk y / mω c .