Each Landau level is degenerate because of the second quantum number k y, which can take the values k y = 2 π π N L y , where N is an integer. The allowed values of N are further restricted by the condition that the center of force of the oscillator, x 0, must physically lie within the system, 0 ≤ x 0 < L x. This gives the following range for N, 0 ≤ ≤ N < m ω ω c L x L y 2 π π ℏ ℏ .