12/4/2023 0 Comments Hilbert space unbounded statesPearse, E.P.J.: A hilbert space approach to effective resistance metrics. We consider both pure states and quantum mixtures, with particular care for the problems that arise in the latter case. (The reason I say the second issue is "sort of" a physical issue is that the mathematical reason given above actually eliminates this problem: To be rigorous you should always specify first a Hilbert space and then a Hamiltonian, and you will never run into ambiguities like whether the spectrum is discrete or continuous. Symmetric Pairs of Unbounded Operators in Hilbert Space, and Their Applications in Mathematical Physics Download PDF. In this paper we examine, in the framework of Hilbert-space quantum mechanics, the mathematical problem of the existence of the mean value and variance of unbounded observables. the free particle Hamiltonian $H=\frac^n$ and discrete for the torus). Physical reason (sort of): What looks like the same Hamiltonian, e.g. Without knowing a Hilbert space, it doesn't even make sense to speak of an operator on it. Mathematical reason: The Hamiltonian is an operator on a Hilbert space to begin with. There is a mathematical reason and a (sort of) physical reason:
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