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Results tagged with operators
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user 197014
In physics, an operator is almost always either a square matrix or a linear mapping between two function spaces (defined on, say, $\mathbb R^n$). Operators serve as observables and as time evolution operators in Quantum Mechanics. This tag will most often find valid use in quantum mechanics; don't use this tag just because your equations contain "everyday operations" like $\times$, $+$!
1
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Adjoint of an operator
Suppose $\mathcal{H}$ is a Hilbert space, and suppose $A : \mathcal{D}(A)\subset \mathcal{H}\rightarrow\mathcal{H}$ is a linear operator on a dense subspace $\mathcal{D}(A)$ of $\mathcal{H}$. Then $y\ …
1
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Spectral theorem for unbounded self-adjoint (hermitian) operators
The original source of the spectral theorem for unbounded self-adjoint operators was John von Neumann, who was a student of Hilbert. … operators; he formulates abstract boundary conditions and discusses how to obtain a self-adjoint operator from the adjoint of a symmetric operator by imposing such conditions. …
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Physical significance of no self-adjoint momentum operator on half line?
From a Mathematician's perspective, you can define a "momentum" operator on the half line, but you need to allow 2d vector functions instead of scalar functions. The problem is that differentiation on …
2
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Accepted
Real eigenvalues of continuum spectrum of a self-adjoint operator
Suppose $\mathcal{H}$ is a complex Hilbert space. A general selfadjoint operator $A : \mathcal{D}(A)\subset\mathcal{H}\rightarrow\mathcal{H}$ has a linear domain $\mathcal{D}(A)$ that is dense in $\ma …