# Finding Wavefunction with just the Hamiltonian

1. May 15, 2015

### metapuff

Say I have a wavefunction that's a superposition of two-particle states:
$$\Psi = \int dk ~f(k) c^{\dagger}_k c^{\dagger}_{-k} | 0 \rangle$$
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
$$f(k) = \langle c_{-k}c_k | \Psi \rangle$$
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. May 15, 2015

### MisterX

No, it's not possible without more information. There are infinite possibilities for $f(k)$ and each possibility corresponds to a different state.