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I am having trouble with problem 5.32 of Griffiths Quantum mechanics 3rd edition. The problem consider a free electron gas in which number of spin up and down particles is different and asks for the effect that it will have on the total energy. The difficulty I am having is that I don't get why that would affect the total energy I mean the problem considers the case in which there is no magnetic field so I am not sure why total energy would be different. As far as I understand net magnetic dipole has effect on total energy only in presence of magnetic field. I don't need the whole solution it would be great if someone could tell me where I am going wrong.

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  • $\begingroup$ Probably each electron has to use some quantum state and that quantum state can be shared by two electrons of opposite spin, but not by two electrons of same spin. $\endgroup$
    – Ján Lalinský
    Aug 24, 2019 at 20:47

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