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Many particle wavefunction

  • Thread starter Brewer
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  • #1
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If in the case of two non-interacting particles, the wavefunction looks like (for bosons):

[tex]\psi(x_1, x_2) = \frac{1}{\sqrt{2}}[\phi_a(x_1)\phi_b(x_2) + \phi_a(x_2)\phi_b(x_1)[/tex]

And to normalise the wavefunction, the modulus squared has to be found. I can do this when I can substitute standard wavefunctions into the equations (either harmonic oscillator, or a square well for example), but I've been looking at exam papers and in questions with this kind of question, no wavefunctions are given and the answer (its normally a "show that..." question) is still given in terms of phi 1 and phi 2.

I'm unsure how the modulus squared bit works when I don't know for sure that the answer is complex. I also don't know how to integrate these without substituting values in for the wavefunctions. Any help going through this would be appreciated.
 

Answers and Replies

  • #2
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It's been a long time since I've done any many-particle qm. But I can tell you that you definitely cannot integrate without knowing the wavefunctions. However, there may be some mention that the single-particle wavefunctions (i.e. the phi's) are themselves normalized. Then you know that e.g.
[tex]\int |\phi_a|^2 dx = 1[/tex], so you likely don't have to do any integrals explicitly.
 

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