Question

Sketch the probability density graph (not normalized) for a particle in a ground-state box (n = 1)

Answer 1

The non-normalized wave function of the particle in a box of length L, in ground state(n=1) is given by

where is the normalisation constant.

The probability density is

$P(x)=|\psi(x)|^2=|A|^2 \sin^2 \Big( \frac{\pi x}{L}\Big)$

The plot of is shown below

Plot of ground state probability density of particle in a box P(x)