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Correlation between two particles problem

  • Thread starter 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!?
 

Answers and Replies

  • #2
Dick
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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!?
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?
 

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