Show that for a particle of mass $m$ which moves in a one-dimensional infinite potential well of length $a$, the uncertainties product $\Delta x_{n} \Delta p_{n}$ is given by $\Delta x_{n} \Delta p_{n} \simeq n \pi \hbar / \sqrt{12}$.
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Step 1
The potential \( V(x) \) is zero inside the well (i.e., \( 0 \leq x \leq a \)) and infinite outside. The time-independent Schrödinger equation for this system is given by: \[ -\frac{\hbar^2}{2m} \frac{d^2 \psi(x)}{dx^2} = E \psi(x) \] Show more…
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