Past exam of the mathematics course of the University of Cambridge / 2022 / ib / Paper 2 / 15B / b / i

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- Solution i

Solution

Expand the normalized initial wavefunction in the orthonormal energy basis:

c_{n} = \int_{0}^{a} χ_{n} (x)^{*} f (x), d x .

The Time-dependent Schrodinger equation then gives the unitary time evolution

ψ (x, t) = n = 1 \sum \infty c_{n} χ_{n} (x) e^{- i E_{n} t /ℏ} .

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