 Solution

ID: past-exam-of-the-short-options-paper-shared-by-prelims-and-parts-a-and-b-of-the-physics-course-of-the-university-of-oxford/2012/s3/3/4/solution

Projection onto the antisymmetric quantum superposition gives amplitude

\frac{1}{2} (e^{- i E_{1} t /ℏ} - e^{- i E_{2} t /ℏ})

. Its squared modulus is

P_{+ \to -} (t) = sin^{2} (\frac{( E _{2} - E _{1} ) t}{2ℏ}) .

It vanishes initially, reaches one at a half-recurrence time, and returns to zero after

τ

. This interference depends on a relative phase even though each energy-eigenstate population and the mean energy remain constant.

 New to topics? Read the docs here!