Sunday, December 11, 2016

quantum mechanics - Is there any non-hermitian operator on Hilbert Space with all real eigenvalues?


The property of hermitian is the sufficient condition for eigenvalue being real. Is there any non-hermitian operator on Hilbert Space with all real eigenvalues? If there exist, then can all eigenstates be orthogonal to each other? And these operators have any application in Quantum mechanics?




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