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at the moment I got a bit confused about the notation in some QM textbooks. Some say the operators should be symmetric, some say they should be self-adjoint (or in many cases hermitian what maybe means symmetric or maybe self-adjoint). Which condition do we need for our observables (cause they are not the same in the case of an infinite-dimensional Hilbertspace)?

If symmetric is enough why can we find an othonormal basis of eigenvectors (since the spectral theorem holds only for self-adjoint operators)?

Thanks for your help

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# I Symmetric, self-adjoint operators and the spectral theorem

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