 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/s18/3/1/solution

In the source's Gaussian electromagnetic units, set

Π = - i ℏ \nabla - e A / c

and take

Φ = 0

. Then

H_{D} = c α \cdot Π + β m c^{2} = (m c^{2} I c σ \cdot Π c σ \cdot Π - m c^{2} I) .

The chosen gauge is independent of

x, z, t

, so simultaneous energy and canonical

p_{x}, p_{z}

eigenstates justify the exponential ansatz. On the remaining spinors use

Π_{x} = p_{x} + e B y / c

Π_{y} = - i ℏ d / d y

Π_{z} = p_{z}

. The coupled equations are

(E - m c^{2}) φ = c σ \cdot Π χ

and

(E + m c^{2}) χ = c σ \cdot Π φ

 New to topics? Read the docs here!