Hello! I have a proof in my QM book that: ##\left<r|e^{-iHt}|r'\right> = \sum_j e^{-iHt} u_j(r)u_j^*(r')##, where, for a wavefunction ##\psi(r,t)##, ##u_j## 's are the orthonormal eigenfunctions of the Hamiltonian and ##|r>## is the coordinate space representation of ##\psi##. I am not sure I understand this. Like in general ##\psi = \sum_j a_j u_j## and I don't know where the ##a_j##'s disappeared. Also I am not sure what is the relation between ##u_j(r)## and ##u_j(r')##. Is there any formula linking them? Thank you!(adsbygoogle = window.adsbygoogle || []).push({});

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# I Notation in QM

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