A problem based on Quantum Physics 2

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SUMMARY

The discussion focuses on determining the minimum time required for a wave function, ψ(x), of a particle in a stationary state with energy Eo to return to its original form. The user proposes that the time can be calculated using the equation t = 2πh/Eo, derived from the relationship Eot/h = 2π. Additionally, they seek a more rigorous analytical method to confirm this result, suggesting the solution to the equation e^(iE0t/ħ) = 1 as a potential approach.

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Homework Statement



The wave function of a particle in a stationary state with an energy Eo at time t=0 is ψ(x).after how much minimum time the wave function will be ψ(x) again.

Homework Equations





The Attempt at a Solution


ψ(x, t)=φ(x)e^(-iEot/h).intuitively i think the answer should be Eot/h=2π. So t=2πh/Eo.But I am looking for a more rigid analytical method.please help.
 
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That's essentially it. If you want to be more pedantic, you could solve ##e^{iE_0 t/\hbar} = 1## for t.
 

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