Past exam of the physics course of the year 1 of the natural sciences course of the University of Cambridge / 2024 / Paper 1 / Section B / 9 / d

Table of contents
- Solution d

Solution

The position probability density is

p (x) = \frac{2}{L} sin^{2} \frac{2 π x}{L} (0 \leq x \leq L),

and zero outside. It has zeros at

0, L /2, L

and equal maxima

2/ L

at

L /4, 3 L /4

. The two lobes have equal integrated probability. The vertical axis is a density with units of inverse length, not a dimensionless probability at a point.

Figure 1.
Second-state position densities for an infinite well and an illustrative finite well, including evanescent tails
. Details.

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