 Solution

ID: past-exam-of-the-short-options-paper-shared-by-prelims-and-parts-a-and-b-of-the-physics-course-of-the-university-of-oxford/2017/s18/3/5/solution

Separate

x, z

plane waves in the spinless equation. The transverse operator is

- ℏ^{2} d^{2} / d y^{2} + (p_{x} + e B y / c)^{2}

, the same shifted oscillator without a Pauli term. Its eigenvalues are

∣ e ∣ℏ∣ B ∣ (2 n + 1) / c

. Thus

E^{2} = m^{2} c^{4} + p_{z}^{2} c^{2} + ∣ e ∣ℏ∣ B ∣ c (2 n + 1),

which is the printed formula for

B > 0

. The absence of the spin splitting is the substantive difference from the Dirac result.

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