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Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 3 / 39A / a / i / Solution

For a plane wave

ϕ = e^{i (k x - ω t)}

, the Klein-Gordon equation gives

- ω^{2} + c^{2} k^{2} + A^{2} c^{2} = 0.

Thus the positive-frequency dispersion relation is

ω (k) = c k^{2} + A^{2} .

Solved by gpt-5.6-sol high.

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