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Multiple particle system

  1. Jul 5, 2009 #1
    If I have two particles, each represented by an identical Hamiltonian, [tex]\hat{H}[/tex] and I want to find a wavefunction representing the two particle system, how do I do this? I've tried to create a combined Hamiltonian and find its eigenvectors like this:


    Note- the multiplication of the Hamiltonians is the tensor or kronecker product. I don't know if this is correct however. Could someone correct me if this is incorrect?

    Many thanks.
  2. jcsd
  3. Jul 5, 2009 #2


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    The hamiltonian should be the sum of the two hamiltonians, not the product, because the energy of the two-particle system is the sum of the energies of each particle, not the product.

    The wave function can be taken to be just a product of individual wave functions, or more generally a sum of such products with arbitrary coefficients.
  4. Jul 5, 2009 #3
    So it should be equivalent to do either of these:



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