Why sometime we use the integral to expand the eigenstates and sometime we use the sum to expand? now i am read the modern quantum mechanics J.J.Sakurai text and confusing
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Related: https://physics.stackexchange.com/q/9551/2451 and links therein. – Qmechanic Nov 01 '17 at 12:34
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Also related: https://physics.stackexchange.com/q/359965/50583 – ACuriousMind Nov 01 '17 at 13:43
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Sometimes eigenvalues form a discrete spectrum,such as discrete energy levels in a potential well,so we use sum.But sometimes they form a continous spectrum,such as momentum of free particle,so we use the integral.
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And sometimes both (for instance, in an atom there are discrete energy levels but also a continuum of unbound states in which the electron is free) – zeldredge Nov 01 '17 at 14:00