To find the energies, note that translating the harmonic oscillator potential does not affect the energies. The energies of this system are thus identical to those of the standard quantum harmonic oscillator, E n = ℏ ℏ ω ω c ( n + 1 2 ) + p z 2 2 m , n ≥ ≥ 0 . The energy does not depend on the quantum number k y, so there will be a finite number of degeneracies (If the particle is placed in an unconfined space, this degeneracy will correspond to a continuous sequence of p y ). The value of p z is continuous if the particle is unconfined in the z-direction and discrete if the particle is bounded in the z-direction also. Each set of wave functions with the same value of n is called a Landau level.