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# Questions tagged [notation]

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### Taking the Hamiltonian eigenvalue problem into position space?

I'm having a hard time notationally understanding the relationship of: $$\hat{H} \vert{\psi}\rangle = E\vert \psi\rangle$$ and $$\hat{H} \psi(x) = E\psi(x)$$ Here's my thought process: Starting ...
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### Question about Einstein summation convention

I'm dealing with the following: $$\eta^{\alpha \mu} \eta_{\alpha \nu} \phi,_{\beta \mu}$$ $$\eta^{\alpha \beta} \phi,_{\alpha \beta}$$ where $\eta$ is the Minkowski metric and $\phi$ is a function ...
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### Confusion about expressing an inner product using the Einstein summation convention

I think this likely comes down to the following expression, $$g’^{ab}e’_a e’_b = \delta ^a_b$$ Is this in agreement with the Einstein summation convention? Because even though the two indices are ...
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### Why can we 'act on the left' with an operator?

This comes from notes on perturbation theory I am learning in class. I have seen this a few times but never really understood it: how is it that we can apply an operator to the conjugate state on the ...
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### What does it mean “differentiation with respect to the coordinates of particle 1 or 2”?

I was reading Introduction to Quantum Mechanics by Griffiths. In Chapter 5, Identical Particles, I came across the notation $\nabla_1$ and $\nabla_2$. Griffiths writes that it means "differentiation ...
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### How to further expand $\text{grad} \left( \vec{a} \cdot\vec{b} \right ) = \vec{\nabla} \left (\vec{a} \cdot\vec{b} \right )$? [migrated]

With $\vec{a}, \vec{b}: \mathbb{R}^3 \to \mathbb{R}^3$ vector fields: I want to expand $\text{grad} \left( \vec{a} \cdot \vec{b} \right ) = \vec{\nabla} \left (\vec{a} \cdot \vec{b} \right )$. So I ...
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### Why is the ångström not a metric unit? And why is the ångström spelt with the Scandinavian letters “å” and “ö”?

The website here http://unitsofmeasure.org/ucum.html tells us whether every unit is metric or not. Metric units can be multipled by a power of 10 and can be combined with a prefix. 1 ångström is ...
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### Is there a database summarizing common notations? [closed]

Is there a database summarizing common notations? For example I read the symbol $\kappa$ and want to know which meanings are common e.g. sorted by different areas of science? I know that I could just ...
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### How do you read the spin contributions of proton

This paper reads the number of their results. I'm attaching the how they have included all the spin contributions of quarks to proton. The contributions are from u, d, s quarks. How I can tell ...
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### Spring constant of harmonic oscillator [closed]

I got a task from my lecturer to solve a differential equation for a simple harmonic oscillator: $$m{d^2\vec{r} \over dt^2}=-k^2\vec{r}.$$ So far, I have managed to find this equation only in one book....
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### Is there a notation alternative to Hertz?

Hertz, as we all know, is a unit of frequency where 1 Hz equals one cycle per second. Conversely ...
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### A simple notation problem (bra ket notation) [closed]

How can it change this to that?
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### If $\mathrm df$ is an inexact differential, how would the function $f$ look like?

I am studying thermodynamics and in the first chapter the concept of exact and inexact differentials were used to talk about the differences between internal energy, work and heat. From Blundell and ...
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### Bra-ket notation in a 3 dimensional system

Recently we started to learn quantum mechanics in a three-dimensional system. However, I am very confused from the beginning. Firstly, professor told us that for a position vector $\pmb{x}={}^t(x,y,z)$...
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### Did R. Feynman know about the different notations for exact and inexact differentials? [closed]

I remember reading a long time ago, the story of a student taking R. Feynman for responsible of her (I think it was a woman, not sure though) fail at an exam of physics because what was written in her ...
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### How can uncertainty be represented as a chance [closed]

How can uncertainty be represented as a chance when we write in Heisenberg's principle? Why do we use Delta for uncertainty and mathematically use it the same way as if it was a change in position or ...
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### Position operator acting on wavefunctions. Why is $\left<x\right|\hat{X}\left|{\psi}\right> =\hat{X} \left<x|{\psi}\right>$?

Gennaro Auletta in his book makes the following argument to show that multiplicative operator acting on his eigenvectors acts in a multiplicative way on eigenfunctions as well. Here's the argument. ...
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### What is the value of the inner product $_x\langle+|-\rangle$? [closed]

I know that $\left|_x\langle+|-\rangle\right|^2 = 1/2$, so is it just as simple as taking the square root of $1/2$? Thanks.
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### The spinor metric, basic spinor calculations and spinor indices

I'm currently reading the textbook "Finite Quantum Electrodynamics" by Günter Scharf, but I find myself stuck already on page 24. Background Scharf introduces the index-raising symbol (spinor metric)...
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### What does $\Delta$ stand for? [duplicate]

Newton’s first law states that $\Delta v=0$ unless acted on by an external force, $F_{\mathrm{net}}\neq0$. Can someone explain to me what the $\Delta v$ symbol means?
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### Einstein solid degree of freedom

I was studying from Schroeder's thermal physics book. When it talks about Einstein solids it says that they have 2 degrees of freedom thus $U=NkT$ However, I thought when we talk about Einstein ...
I am learning SR, and don't understand the difference between the following notations of a Lorentz transformation $\Lambda$ $$\Lambda_{\mu\nu} , \Lambda_{\mu}\ ^\nu , \Lambda^{\mu\nu}$$ I know that ...
I am new to QFT and have to catch up with some things that I did not learn from my SR courses. I am learning about the tensor notation, in particular the metric tensor, g_{\nu\mu}=g_{\mu\nu}=\begin{...