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

  • Thread starter agooddog
  • Start date
  • Tags
    Qm System
In summary, the conversation discusses a system of two particles in a superposition of states with definite energies. The question is how long it takes for the wave function to return to its initial state at t=0. The energy-time uncertainty principle is mentioned as a possible equation to use. There is also mention of orthogonality between the particles' initial states and a cosine term in the time-dependent version of the wave function. The question is posed whether the system returns to the state of t=0 when the cosine term equals 2pi. The conversation ends with a request for the calculations to be shown and a question about whether this is actually a two-particle system or a single particle in a superposition.
  • #1
agooddog
3
0

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.
 
Physics news on Phys.org
  • #2
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.
 

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

What is a two-particle system in Quantum Mechanics?

A two-particle system in Quantum Mechanics refers to a system that contains two particles interacting with each other. These particles can be anything from atoms to subatomic particles, and their behavior is described by the laws of Quantum Mechanics.

What are the properties of a two-particle system?

The properties of a two-particle system are described by the wave function, which contains information about the position, momentum, and spin of each particle. The wave function also determines the probability of finding each particle in a particular state.

How do two particles interact in a quantum system?

In a quantum system, two particles can interact through a force or through the exchange of virtual particles. This interaction is described by the potential energy between the particles, which is related to the wave function and determines the probability of different outcomes for the system.

What is entanglement in a two-particle system?

Entanglement in a two-particle system refers to a phenomenon where the properties of two particles become correlated and cannot be described independently. This means that the state of one particle is dependent on the state of the other, even if they are physically separated.

Can a two-particle system violate the laws of classical physics?

Yes, a two-particle system can exhibit behaviors that cannot be explained by classical physics. This is because in Quantum Mechanics, particles can exist in multiple states simultaneously and can also be entangled, which goes against the principles of classical physics.

Similar threads

Two-level Quantum System - initial state
Replies
14
Views
2K
Finding the Ratio of Particles in a Three-Level Quantum System
Replies
1
Views
2K
How to Find the Canonical Partition Function for Two Quantum Particles?
Replies
5
Views
1K
Electric sinusoidal field on a hydrogen atom - Quantum Mechanics
Replies
3
Views
955
Composite Spin 1/2 System Probability Question
Replies
3
Views
2K
Entropy of a generalised two-state quantum system
Replies
1
Views
2K
How Does Coulomb Repulsion Affect a Fermionic Two-Level System?
Replies
1
Views
1K
Is the given wave function a stationary state?
Replies
3
Views
2K
Why are unperturbed states valid basis for perturbed system?
Replies
4
Views
1K
Understanding the Energy States of a Particle in a Finite Potential Well
Replies
7
Views
2K

Hot Threads

Recent Insights

Back
Top