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Results tagged with commutator
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user 251599
A mathematical construct quantifying the difference in effect of applying two operators in two alternate successions. It is the defining product of a Lie algebra, the efficient underlying description of Lie groups, of use in several areas of physics, most notably quantum field theory.
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Do the number operator and general Hamiltonians commute?
In a proof of the equivalence of the canonical and grand canonical ensembles (in the thermodynamic limit) in Jochen Rau's Statistical Physics and Thermodynamics (highly recommended!), the author evalu …
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If an operator commutes with the Hamiltonian then do all of its projectors commute also?
Suppose I have an (self-adjoint) operator (representing an observable) $O$ which commutes with the system Hamiltonian $H$. Does it follow that $[P_O(\Delta),H] = 0$ where $P_O(\Delta)$ is an arbitrary …
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Commuting normal operators have common eigenbasis?
One often finds in quantum mechanics textbooks (for physicists) a "proof" that self-adjoint and commuting operators $A,B$ have a common eigenbasis. However, in the standard proof of Bloch's theorem (s …
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Showing that time ordering does not matter for the measurement of commuting observables
Suppose I have two observables $R$ and $S$ who are represented by operator $R$ and $S$ which commute (I will hereafter ignore the distinction between observables and the operators representing them), …
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Why can't commuting operators allow for full state determination?
For the purposes of this question, suppose that the operator $R$ representing the observable $\mathsf{R}$ has nondegenerate eigenspaces.
In discussing state determination (for some given situation, ho …
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