Verifying Energy-Time Uncertainty Principle for Particle in Infinite Well

[Gale]

Consider the wavefunction: particle in an infinite well of width L, with
wavefunction given as a superposition of two energy eigenstates, with quantum numbers n=1 and m=2. Show that the Energy-Time uncertainty principle, applied to the time it takes <x> to change by an
amount σx, indeed holds true in this case.

soo, i have <x> and σx, and i guess i can find σE by doing sqrt(<E>^2 + <E^2>), i just don't see how I'm supposed to use those values for the uncertainty principle which says ΔE*Δt< hbar/2.

help?

 

[quantumdude]

soo, i have <x> and σx,

OK so you should have $<x>$ as some function of $t$, right? So set the problem up like this (insert the function of time you found in place of my $f(t)$).

$$<x>=f(t)$$

$$<x>+\sigma x=f(t+\Delta t)$$

From there you are supposed to solve for $\Delta t$.