Q2(b). Particle in a box: probability in the first 1/a of the width
A particle is in the nth energy state, φn(x), of an infinite square well potential with width L (box size from 0 to L). Calculate the probability that the particle is confined to the first 1/a of the width of the well.
Answer in brief
Pn(a) = ∫₀L/a φn² dx = 1/a − (1/2nπ) sin(2nπ/a): the classical value 1/a, less a wave term that dies away as 1/n.
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Coversparticle in a boxinfinite square wellprobability densityBorn interpretationcorrespondence principle
All parts of Question 2
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- 2(b) Particle in a box: probability in the first 1/a of the width20 marks
- 2(c) Simple cubic cell from the (100) reflection; room for an interstitial atom20 marks