Why in quantum mechanics do we require that the state space be a Hilbert space rather than just an inner product? Does the completeness of the norm have any clear physical role?
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Possible duplicates: http://physics.stackexchange.com/q/20822/2451 , http://physics.stackexchange.com/q/169767/2451 , http://physics.stackexchange.com/q/41719/2451 and links therein. – Qmechanic May 04 '15 at 15:02