quantum mechanics - Why electron can not be found at some node locations in the infinite potential well?

Consider electron in an infinite potential well, studied in quantum mechanics. Position probability density of the electron is

$$P_n(x)=\left(\frac{2}{L}\right)\sin^2\left(\frac{n\pi x}{L}\right)$$

where $0\leq x\leq L$ and $L$ is length of the box.

So for $n>1$, probability density & hence probability of finding location of the electron at certain $x$ is $0$. The electron moves from left to right & right to left between the walls of the well. So Mathematics says that electron can not be found at certain $x$ node locations within the box; which is very strange. But is there any experimental evidence for this? While crossing these special $x$ node locations, as if electron disappears from the box. This is very absurd.

My question is: Is this a just mathematical result (without any reality) or a physical reality/actuality?