Correlation between two particles problem

In summary, the problem involves a physical system of two particles in an infinite potential well. Each particle has its own Hamiltonian, with corresponding eigenstates and eigenvalues. The global system has a basis composed of states defined by a tensor product of the two particle states. The problem asks for the eigenstates and eigenvalues of the total Hamiltonian and the degeneracy of the lowest two levels. A hint to start solving the problem is to consider the two lowest energy states and the different ways they can be occupied.
  • #1
EEnerd
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Homework Statement



Consider a physical system made of 2 particles , particle (1) and particle (2)of the same mass m, which don’t interact with each other and which are both placed in an infinite potential well of width a. Denote H(1) and H(2) the Hamiltonians of each particles by |ψ1> and |ψ2> the corresponding eigenstates of the first and second particle with energy (n*pi *hbared)^2 /2m(a^2), and (q*pi*h bared)^2/2m(a^2). In the state of the global system the basis chosen is composed of states |ψn ψq> defined by
|ψn ψq>=|ψn(1)> (tesla product) |ψq(2)>
What are the eigen states and eigen values of the H=H1+H2( total Hamiltonian) and give the degeneracy of the lowest two levels?!

its quantum mechanics cohen p.g 348

Homework Equations





The Attempt at a Solution

I have no idea how to start, i took yesterday and its on my final on Thursday, just a hint on how to start!?
 
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  • #2
EE said:

Homework Statement



Consider a physical system made of 2 particles , particle (1) and particle (2)of the same mass m, which don’t interact with each other and which are both placed in an infinite potential well of width a. Denote H(1) and H(2) the Hamiltonians of each particles by |ψ1> and |ψ2> the corresponding eigenstates of the first and second particle with energy (n*pi *hbared)^2 /2m(a^2), and (q*pi*h bared)^2/2m(a^2). In the state of the global system the basis chosen is composed of states |ψn ψq> defined by
|ψn ψq>=|ψn(1)> (tesla product) |ψq(2)>
What are the eigen states and eigen values of the H=H1+H2( total Hamiltonian) and give the degeneracy of the lowest two levels?!

its quantum mechanics cohen p.g 348

Homework Equations





The Attempt at a Solution

I have no idea how to start, i took yesterday and its on my final on Thursday, just a hint on how to start!?

It's a 'tensor' product, not a 'tesla' product. But I really wouldn't worry about that. What are the two lowest energy states and how many ways can you pick n and q to occupy each one?
 

FAQ: Correlation between two particles problem

What does it mean when two particles are said to be correlated?

When two particles are correlated, it means that there is a relationship between their properties or behaviors. This can manifest in many ways, such as the particles having similar energies, moving in the same direction, or being connected in some way through a force.

How is the correlation between two particles measured?

The correlation between two particles can be measured using statistical methods, such as calculating the correlation coefficient or performing a regression analysis. These methods can quantify the strength and direction of the relationship between the particles.

What factors can affect the correlation between two particles?

There are several factors that can affect the correlation between two particles. These include the distance between the particles, the strength of the force between them, and any external influences or interactions that may be present. Additionally, the properties of the particles themselves, such as their mass or charge, can also impact their correlation.

Is there a limit to how strongly two particles can be correlated?

Yes, there is a limit to how strongly two particles can be correlated. This limit is known as the Bell's inequality and is based on the principles of quantum mechanics. According to this theory, the correlation between two particles cannot exceed a certain value, no matter how close or strongly connected they may be.

How is the correlation between two particles relevant in scientific research?

The correlation between two particles is crucial in many areas of scientific research, particularly in fields such as quantum mechanics, particle physics, and cosmology. It helps us understand the behavior and interactions between particles, which in turn can lead to advancements in technology, medicine, and our understanding of the universe.

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