How Long Until a Two-Particle Quantum System Reverts to Its Initial State?

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SUMMARY

The discussion centers on determining the time it takes for a two-particle quantum system, represented by the wave function Psi(one) + Psi(two), to revert to its initial state at t = 0. The key concept involves the energy-time uncertainty principle and the orthogonality of the particles' initial states. The user suggests that the system remains in a stationary state due to definite energies E(1) and E(2), but acknowledges the complexity introduced by the cosine term in the time-dependent wave function. The conclusion is that the system returns to its initial state when the cosine term equals 2π, indicating a periodic behavior.

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Homework Statement



This is a quick one, which I apologize ahead of time for not writing this out more neatly. The parentheses denote subscripts. I have a system of two particles, which are in a superposition Psi(one) + Psi(two). The energy of particle one is E(1) and of particle two is E(2). How long does it take for the wave function of the system of two particles to return to what it was at t = 0?

Homework Equations



Perhaps the energy-time uncertainty principle.

The Attempt at a Solution



Well, alright. My first reaction is to say that because there are definite energies, it is in a stationary state and will not change with time. However, getting to the math of it, this only works if there is orthogonality between the two particles' initial states. When normalizing the time-dependent version, I end up with a cosine term at the end. Does the system return to the state of t = 0 when the term in the cosine = 2pi ?

I feel like I'm on the right track but it seems kind of messy.
 
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Are you sure this is a two-particle system? Or is it a single particle in a superposition of energy eigenstates?

It would help if you showed your calculations.
 

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