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Consider a particle in a box of the form

##V(x)=

\begin{cases}0 \; \; \; -L < x < 0\\

V_0 \; \; \; 0<x<L\\

\infty \; \; \; \text{ elsewhere}.\end{cases}##

One can show that the probability density

##P(x) = \Psi^* \Psi## is greater in the region of lower kinetic energy (that is at higher potential energy).

What's the physical explanation for this? My notes say something along the lines of "lower velocity give higher probability density" which seems very vague.

I'm guessing this is also related to how the Boltzmann distribution, where the probability decreases with the energy.

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# I Probability density and kinetic

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