# Tagged Questions

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### Basis in quantum mechanics

My quantum mechanics textbook (Primer of Quantum Mechanics, by Marvin Chester) says that both the momentum space and the position space are basis spaces. It also says that the momentum space is ...
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I've been solving a problem in quantum mechanics, and I was deriving the standard deviation of $P$, knowing that $\langle P\rangle=0$. Because $\Delta P=\sqrt{\langle P^2 \rangle - \langle P \rangle ... 1answer 145 views ### Justification for smeared fields in the Wightman axioms? I just started reading PCT, Spin and Statistics, and All That. Can someone explain why we use operator valued distributions to describe fields? I read somewhere that it would take infinite energy to ... 2answers 271 views ### What is the most general expression for the coordinate representation of momentum operator? I have a question about deriving the coordinate representation of momentum operator from the commutation relation,$[x,p]= i$. One derivation (ref W. Greiner's Quantum Mechanics: An Introduction, 4th ... 2answers 1k views ### Translator Operator In Modern Quantum Mechanics by Sakurai, at page 46 while deriving commutator of translator operator with position operator, he uses $$\left| x+dx\right\rangle \simeq \left| x \right\rangle.$$ But for ... 4answers 673 views ### Is the momentum operator diagonal in position representation? The matrix elements of the momentum operator in position representation are: $$\langle x | \hat{p} | x' \rangle = -i \hbar \frac{\partial \delta(x-x')}{\partial x}$$ Does this imply that$\langle x ...
I have two related questions on the representation of the momentum operator in the position basis. The action of the momentum operator on a wave function is to derive it: \hat{p} ...
Let us divide the time $T$ into $N$ segments each lasting $δt = T/N$. Then we write $\langle q_F | e^{−iHT} |q_I \rangle = \langle q_F | e^{−iHδt} e^{−iHδt} . . . e^{−iHδt} |q_I \rangle$ Our ...