# Tagged Questions

In physics, an operator is almost always either a square matrix or a linear mapping from one space of functions (often on $\mathbb{R}^N$ or $\mathbb{C}^N$) to the same or other like space of functions. Operators serve as *observables* and as *time evolution operators* in Quantum Mechanics. This tag ...

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### Construct any Hamiltonian that is the linear combination of existing constructable Hamiltonians

In the paper Quantum Computation over Continuous Variables, it states that since $$e^{iAt}e^{iBt}e^{-iAt}e^{-iBt} = e^{-[A,B] t^2} + O(t^3)$$ when $t\rightarrow 0$, if one can apply a set of ...
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### Single particle tunneling Hamiltonian

In reference to Problem 9, Chapter 2 in Modern Quantum Mechanics by JJ Sakurai, For a single particle tunneling in a 1D double well potential, with position eigenkets $\mid R\rangle$, $\mid L\rangle$....
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### Three dimensional isotropic harmonic oscilator Hamiltonian

Let us consider the Hamiltonian for the isotropic three dimensional harmonic oscilator: $$H = \dfrac{\mathbf{P}^2}{2m}+\dfrac{m\omega^2\mathbf{R}^2}{2},$$ where $\mathbf{P}$ and $\mathbf{R}$ are the ...
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### Physical significance of non-commutativity of ladder operators in Quantum Harmonic Oscillator

If we apply the raising (creation) operator to $Ψ_n(x)$ and the apply to it the lowering (annihilation) operator, we get $Ψ_n(x)$ times a constant. Does it physically say something? Can we get any ...
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### Does Operator Product Expansion form an algebra?

The operator product algebra in CFT is defined as $$\mathcal{O}_i(z,\bar{z})\mathcal{O}_j(\omega,\bar{\omega}) = \sum_{k} C^k_{ij}(z-\omega,\bar{z}-\bar{\omega})\mathcal{O}_k(\omega,\bar{\omega}).$$ ...
### Can I always find an unitary operator $B$ such that $\{A,B\}= 0$ for a given, unitary operator $A$?
Considering an arbitrary unitary operator $A$, what is the least criteria this operator must satisfy in order that it is possible to find at least another unitary operator $B$ that anti-commutes with ...