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Finding Wavefunction with just the Hamiltonian

  1. May 15, 2015 #1
    Say I have a wavefunction that's a superposition of two-particle states:
    [tex] \Psi = \int dk ~f(k) c^{\dagger}_k c^{\dagger}_{-k} | 0 \rangle [/tex]
    Here, ##|0\rangle## is the vacuum and ##c^{\dagger}_k c^{\dagger}_{-k} | 0 \rangle## represents a pair of fermions with momenta ##k,-k##. My goal is to solve for the coefficients ##f(k)## that determine the weight of each two-particle state in the superposition. Presumably, I could do this by computing
    [tex] f(k) = \langle c_{-k}c_k | \Psi \rangle [/tex]
    However, I don't know what ##\Psi## is. I do know the form of the Hamiltonian for this system, though. Is it possible to find ##\Psi## if I only know the Hamiltonian ##H## and the form of the basis states ##c^{\dagger}_k c^{\dagger}_{-k} | 0 \rangle##? Thanks in advance! :)
     
  2. jcsd
  3. May 15, 2015 #2
    No, it's not possible without more information. There are infinite possibilities for ##f(k)## and each possibility corresponds to a different state.
     
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