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

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- Solution a

Solution

For the one-dimensional quantum harmonic oscillator,

i ℏ \frac{\partial ψ}{\partial t} = (- \frac{ℏ ^{2}}{2 m} \frac{\partial ^{2}}{\partial x ^{2}} + \frac{1}{2} m ω^{2} x^{2}) ψ .

This is the Time-dependent Schrodinger equation with harmonic potential.

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