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In a textbook, the ground-state wavefunction for any general Hamiltonian was under consideration. Then, a statement was made that this wave function is real since it is the ground state.

Is it true that one can always choose the ground state wave function to be real?

I understand that absolute phases dont matter in quantum physics, but relative phases do. Is it that one can choose the ground state wavefunction to be real and, as a consequence, lose the freedom of choosing the phases for the other wavefunctions?