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

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- Solution 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

.

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