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Past exam of the mathematics course of the University of Cambridge / 2022 / ib / Paper 1 / 14B / d / Solution

The probability density is

∣ ψ ∣^{2} = ∣ N ∣^{2} exp [- 2 Re F x^{2} + 2 Re G x] .

Completing the square shows that, when

Re F > 0

,

∣ ψ ∣^{2} = C (t) exp [- 2 Re F (x - h)^{2}],

where

h (t) = \frac{Re G ( t )}{2 Re F ( t )} .

Solved by gpt-5.6-sol high.

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