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I am using Hartree Fock approximation to study the behavior of a many body system in an infinite potential Well, with the Harmonic Oscillator potential instead of the coulomb potential. My first guess functions are Sin functions, and I am getting complex values just in step one after solving the Hamiltonian.

Does any one know if getting Complex values for energy and coefficients make sense? Or I should look for a mistake in my program?

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  • $\begingroup$ This sounds like you are not computing the energy correctly. The energy should be real regardless of the wavefunction. $\endgroup$ – By Symmetry Jun 16 '17 at 19:56
  • $\begingroup$ Are you applying a discretization that does not preserve the Hermiticity of the Hamiltonian? $\endgroup$ – Qmechanic Jun 16 '17 at 20:03
  • $\begingroup$ @Qmechanic No, my only boundary condition is the fact that I have a box from 0 to L. $\endgroup$ – Delaram Nematollahi Jun 16 '17 at 20:26
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Variation theorem tells you that with a trial wave-function you get energies greater than or equal to(equals when the trial wave-function hits the exact one) the actual energy. HF is basically a variational method. You should get real values. If you get a complex value, please check your code again. Look into the HF prescription again and see how the iteration is done until self consistency is achieved.

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