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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 $\times$, $+$!

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What exactly is the definition of the representation of an operator in position or momentum ...

I apologize for this kind of silly question, I haven't brushed up on QM for a while. I was looking at a problem today, essentially I'm given some operator $V = \lambda |{\xi}\rangle \langle{\xi}|$ whe …
Abdul Qadeer's user avatar
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Can we find eigenvalues of an operator without knowing the boundary conditions?

Imagine I have a space spanned by the two basis vectors $e_1 = sin x$ and $e_2=cos x$ and I define some inner product using $\langle f|g\rangle = \frac{1}{π}\int_0^{2\pi} f^*g dx$ and some operator $D …
Abdul Qadeer's user avatar