# 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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### Dirac notation - specific acting orientation for operators

I have this doubt: Imagine two operators $A$ and $B$ and the state $\psi$. I know that the following statement is true: $$\langle\psi| A|\psi\rangle^*=\langle\psi| A^\dagger|\psi\rangle$$ But ...
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### Prove that a translation operator times a reflection operator is unitary and Hermitian [closed]

I am trying to prove some properties of the product of the (unitary) translation operator $\hat{T}(a)\psi(x) = \psi(x-a)$ and the (Hermitian) reflection operator $\hat{R} \psi(x) = \psi(-x)$. In ...
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### Relativistic Commutation relation for momentum and position

We all know that the canonical commutation relation give you $$[x_i,p_j]=i\hbar\delta_ij,$$ is there a relativistic version such as $$[x^a,p_b]=i\hbar\delta_a^b?$$ If so what is the time ...
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### Simple QFT simulation - how to do it

I would like to write a simple QFT simulation for a free scalar field with a cubic interaction term. However, I got stuck a bit. I will try to describe what I think I understand. I want to have a ...
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### Is there a physical significance to non-normal states of the algebra of observables?

Quantum theory may be formalized in several different ways. Generally, the physical discussion of different states of a quantum system distinguishes pure and mixed states, and then subsumes both in a ...
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### Closure relation for degenerate eigenkets

Consider an observable in quantum mechanics, with a degenerate eigenvalue in a continuous spectrum. Is it possible for such an eigenvalue to have a finite degeneracy? If the degeneracy is infinite, ...
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### Free Vacuum vs Interacting Vacuum and Wick's theorem

I'm studying perturbation theory in QFT and I stumbled on a conceptual problem. My understanding of the interplay between LSZ reduction formula and the Gell-Mann & Low perturbation series is that:...
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How does operator matrix transform under change of basis? If $\rvert \beta\rangle$ and $\rvert \alpha \rangle$ are two bases related by transformation $\rvert\beta_m\rangle = \sum_n S_{mn} \rvert\... 1answer 128 views ### How to determine the trace and determinat of a differential operator? How to determine the trace and determinant of the operator like$\Box$or$\nabla^2$etc. But first of all how to find the same for the simpler operator$\frac{d}{dx}$? I proceeded as follows. What ... 1answer 58 views ### Deriving the form of generators of transformations I'm struggling to understand a bit of quantum mechanics relating to the transformation generators. This specific bit contains quite a few guesses and assumtions which probably do make sense in ... 1answer 152 views ### Book question positive square root on quantum operator On p.86 Section 2.2.4 of the Quantum computation and quantum information book by Nielsen,$M_{o}$is defined as the positive square root of the positive operator. Is the "positive square root" ... 2answers 231 views ### How the position operator and the position basis are correctly defined? In Quantum Mechanics, if one deals with wave functions, the Hilbert space in question is$L^2(\mathbb{R}^n)$for a particle in$n$-dimensions, and the position operator corresponding to the$i$-th ... 2answers 57 views ### Operator algebra in integral form In QM courses one can quite often see expressions like:$ \langle x| \hat{p} | \psi \rangle = \int dp \langle x| \hat{p} |p\rangle \langle p| \psi \rangle $but I'm a bit confused as to how it ... 1answer 60 views ### Is this treatment of the momentum operator in the Dirac formalism allowed? I have a problem understanding a specific bit of Dirac notation. Take, as an example this derivation: I'm dubious about the step from line 3 to 4. When momentum operator acts on the momentum ... 0answers 47 views ### Determining this vacuum expectation I am trying to find the analytic expression for the result that follows from evaluating this vacuum expectation value:$\langle0\vert;\prod_{i=1}^M \prod_{j=1}^N \hat{a}(y_{ij}) \hat{a}^\dagger(y'_{...
Is there any way to describe phsycially which each creation operator $a^{(i)+}_{n}$ in string theory does to the ground state string? Here would be my guess (although it is likely to be totally wrong)...