Past exam of the mathematics course of the University of Cambridge / 2022 / ib / Paper 4 / 15B / b / iii

Table of contents
- Solution iii

Solution

The phase has unit modulus and

X = x + g t^{2} /2

, hence

⟨ X ⟩_{Θ} = ⟨ x ⟩_{ψ} + \frac{1}{2} g t^{2} .

The free-particle equations imply

⟨ X ⟩ = a + v t

. Therefore

⟨ x ⟩_{ψ} = a + v t - \frac{1}{2} g t^{2} .

The wavepacket centre obeys the classical constant-acceleration trajectory, an instance of the correspondence principle.

 Ancestors (11)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version