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Quantum Mechanics Notation

Generally we have that $$|\psi\rangle=\int_{all space} \psi(\mathbf x)|\mathbf x\rangle d^3\mathbf x$$ and therefore $\psi(\mathbf x)=\langle\mathbf x|\psi\rangle$. When discussing the mutual ...
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1answer
28 views

Two-component formalism and four-component formalism [closed]

When deriving the Dirac equation for spin-1/2 particles, we realize that the wave function must be four-component. In some works, people use two-component wave function for calculation. So, my ...
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0answers
43 views

Index notation for a Lagrangian with second derivatives

I'm finding the field equations for a hypothetical Lagrangian with dependence on the second derivative of a scalar field, $L\left(\phi,\phi_{,\mu},\phi_{,\mu\nu}\right)$, and in the analogue to the ...
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1answer
37 views

What does $\bar{x}_{\textrm{el}}$ represent?

In the context of centroids and moments, what do $\bar{x}_{\textrm{el}}$ and $\bar{y}_{\textrm{el}}$ represent? For example: $$\bar{x}L = \int \bar{x}_{\textrm{el}}dL$$ Some references that use ...
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0answers
30 views

Notation - d.o.f.'s for Grassmann delta functions in a SUSY field theory amplitude

I was reading the following paper http://arxiv.org/pdf/1306.2962v1.pdf as I stumbled upon an issue concerning counting and assigning the Grassmann degrees of freedom that appear in grassmann delta ...
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1answer
138 views

Reaction coordinate as a function of atomic positions

I'm going over some (molecular dynamics) related literature - specifically the derivation of the Weighted Histogram Analysis Method (WHAM). As a quick backdrop WHAM is a method for stitching ...
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1answer
54 views

What does 400kW(e) mean?

I am trying to read a document and it says a power grid is 400kW(e) what does this mean?
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2answers
182 views

Understanding basic quantum mechanics notation

I was talking with a guy about energy levels of an atom in a magnetic field. He said that energy levels are shifted and that, if you want know how much, you have to analyze this: for 1s state: ...
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2answers
194 views

Correct tetrad index notation

There seems to be some different conventions on the indexes of the tetrad. I am wondering which is the standard, which is correct, and which is an abuse of notation. In Sean Carroll's notes and in ...
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1answer
72 views

Electric flux of a closed surface, $\Psi = Q $ or $\Phi =\int\vec{E}\cdot d\vec{A}$

I have problem with the equation of electric flux. I use one book of fundamental physics and another book of electromagnetic engineering; the two of them give different equations for electric flux. ...
2
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1answer
172 views

QCD color factors from quark gluon vertices

The color factors in QCD tell us the relative strength of the coupling of a quark emitting a gluon, a gluon emitting a quark-antiquark pair or a gluon emitting two gluons. To calculate let them we ...
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1answer
42 views

Apply Hamiltonian to position eigenstates

Let $\hat{H}$ be the free Hamilton operator, is it then true that $$\langle {\bf r}| \hat{H} ~=~ - \frac{\hbar^2}{2m} \Delta \langle {\bf r}|~?$$ Where $\Delta\equiv \nabla^2$. I currently don't see ...
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2answers
55 views

How do I represent $A$ transpose $A$ in indicial notation?

I know this question sounds lame, but the book I am following doesn't use the answer I expect and it has been using a similar notations everywhere else which has confused me. I think Q[Any tensor] ...
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3answers
121 views

Justifying the notation $\langle x\ |\ \psi\rangle$ [duplicate]

I came across this expression: $$\langle x\ |\ \psi\rangle=\psi(x)$$ How can it be justified? I understand the LHS as an inner product, and the RHS just as a function of the parameter $x$.
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2answers
36 views

Interaction Hamiltonian in the interaction picutre

The Schrodinger and Heisenberg pictures make sense to me. But the interaction picture which is a hybrid of the two does not. Author of this text first splits the Hamiltonian up as ...
3
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1answer
187 views

What does $|x⟩|0⟩$ actually mean in bra-ket notation?

Consider the following quote from Wikipedia's page on Shor's algorithm: Initialize the registers to $Q^{-1/2} \sum_{x=0}^{Q-1} \left|x\right\rangle \left|0\right\rangle$ where $x$ runs ...
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1answer
34 views

Meaning the symbol, $W$ and $dW$

What's the difference between $W$ and $dW$? They are both work done and have similar formulae (same dimension). But I don't know the difference between them. $dW$ here ISN'T power.
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3answers
88 views

Suppose $\phi(x)$ is a field, how should I interpret $\partial^\mu\phi$ and $\partial_\mu\phi$?

I am really confused by the sub and upperscript notation sometimes. It might be really trivial but I have a difficult time interpreting the following things in for example this Lagrangian ...
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3answers
81 views

Tensor product in quantum mechanics

In Cohen-Tannoudji's Quantum Mechanics book the tensor product of two two Hilbert spaces $(\mathcal H = \mathcal H_1 \otimes \mathcal H_2)$ was introduced in (2.312) by saying that to every pair of ...
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1answer
39 views

Permutation operator and second quantization

I just read that a permutation operator $P_{i,j}$ acts on a product state $|a_1,...,a_n \rangle \in H^n$ by $$P_{i,j} |a_1,...,a_i,a_j,...a_n\rangle = |a_1,...,a_j,a_i,...a_n \rangle .$$ Now my ...
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2answers
79 views

What are $\mu$ and $\nu$ in $g_{\mu\nu}$ metric?

What are $\mu$ and $\nu$ in $g_{\mu\nu}$ metric? Consider the metric $g_{\mu\nu} = \begin{pmatrix} 1 & 0 &0 \\ 0 & r^2 & 0\\ 0 & 0 & r^2\sin^2\theta \end{pmatrix}$
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4answers
3k views

What does Peter Parkers formula represent?

Okay, so the trailer for the new Spider Man movie is out and appearently our friendly physicist from the neightborhood came up with something. However I can't find out what this is. Transcription: ...
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1answer
46 views

What does a colon mean in hydrodynamics equations?

In some hydrodynamics book I saw a notation like $e:e$ where $e$ is a matrix (shear stress tensor). This double dot product is in a scalar equation, so the result of this operation must be scalar. I ...
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1answer
59 views

Indexed Gradient operator on trigonometric functions

$$\nabla_{i}\nabla_{j}\Big(\frac{\sin(kR)}{R}\Big)$$ Where $R$ is the distance between particle $i,j$. And $k$ is a constant I took $\nabla_{i}=\frac{\partial}{\partial R_{i}}$ and ...
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1answer
94 views

Tensor product notation in quantum mechanics

I'm a bit confused about the use of Tensor products in Quantum mechanics. For instance if two electrons are in the state $\frac{1}{\sqrt{2}}(a(r_1)b(r_2)-b(r_1)a(r_2))\otimes \lvert \downarrow ...
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1answer
60 views

Computation of $T^{\mu\nu}$ from Lagrangian density $\mathscr{L} $

I am trying to understand how upper and lower indices are connected when computing the energy-momentum tensor. In particular, I found the simple problem where the Lagrangian density is given as ...
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1answer
42 views

Energy-Momentum Tensor with mixed indices

I know that $T_{\mu\nu}$ is the Energy-Momentum Tensor and $T=g^{\mu\nu}T_{\mu\nu}$, but does anyone know what $T^{\nu}_{\mu}$ is and how its calculated?
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4answers
531 views

How to indicate that a unit is dimensionless [duplicate]

For my dissertation I am preparing a list of symbols used in the text, which basically is a table that consists of the symbol, a short explanation and the dimension it has as indicated below: ...
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1answer
48 views

Is there a correct yet more compact way to write these equations?

I've got the following equation which denotes the total absorbance $A$ as determined by the sum of the absorbances of individual molecules: \begin{equation} A(\nu,c_{1},...,c_{n}) = \sum_{mol=1}^{n} ...
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1answer
2k views

Meaning of an image on Feynman's shirt

Is there any physical meaning of the image on Feynman's T-shirt?
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3answers
2k views

Is there a physical or mathematical symbol for “happens when”?

How would you denote symbolically, "Equilibrium happens given that ..."?
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0answers
39 views

Is it ever appropriate to write $| \phi(t)>$

I am trying to solve the Schrodinger's wave equation $\hat H |\psi(x,t)> = E|\psi(x,t)>$ using separation variables so that $\psi(x,t) = \psi(x)\phi(t)$ Solving the equation involves the step ...
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1answer
61 views

What does this Hodge dual symbol $\star_3$ mean?

We know that in this $$\star {f(...)}$$ the $\star$ represents the Hodge dual. But in this: $\star_3 f(...)$ what does specifically the $\star_3$ symbol mean?
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5answers
150 views

Is $ds^2$ just a number or is it actually a quantity squared?

I originally thought $ds^2$ was the square of some number we call the spacetime interval. I thought this because Taylor and Wheeler treat it like the square of a quantity in their book Spacetime ...
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6answers
195 views

Is $∣1 \rangle$ an abuse of notation?

In introductory quantum mechanics it is always said that $∣ \rangle$ is nothing but a notation. For example, we can denote the state $\vec \psi$ as $∣\psi \rangle$. In other words, the little arrow ...
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4answers
703 views

Does bra-ket always assume all space?

One thing I never understood about the bracket notation is the limits of the inner product. Given $ \langle \psi∣\psi \rangle$, what can I say about the limits of integration of the inner product? ...
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2answers
88 views

Bra-ket of products

I was trying to solve the following problem. (Lifted from Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory by Szabo and Ostlund) I came across across a solution for ...
8
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1answer
95 views

Group notation $\otimes$ and $\oplus$ used for representations of quarks and mesons

I've been trying to figure out this statement from the PDG quark model summary (PDF). Following $\mathrm{SU}(3)$, the nine possible $q\bar{q}′$ combinations containing the light $u$, $d$, and $s$ ...
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4answers
263 views

What is the right order of creation operators?

I started to learn some basics of second quantisation and specifically its use in quantum chemistry. Currently I'm reading this book by Péter R. Surján, and here is small excerpt from it. If one ...
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0answers
17 views

Proper nuclear reaction notation for arbitrary species

I am wondering the common way to write a nuclear reaction for an arbitrary species. For instance, for neutron capture on a species $X$: $$^{A}_ZX + n \rightarrow ^{A+1}_{\ \ \ \ \ Z}X'.$$ Is this ...
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2answers
71 views

Uncertainty in parenthesis

In a physics text book I read the following: $$e/m=1.758820150(44) ×10^{11} \mathrm{C/kg} $$ In this expression, $(44)$ indicates the likely uncertainty in the last two digits, $50$. How ...
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2answers
178 views

What's the symbol behind Einstein's head? [closed]

What's the symbol called that's behind and to the right of Einstein's head in this picture? Bonus if you can tell me what the whole formula is!
0
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1answer
110 views

Einstein notation in Electrodynamics

I have a question about the notation used in Electrodynamics, for the Eq.6.5.10. Can anyone tell me why is the sign of the covariant derivative swapped when it's transformed to a contravariant ...
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2answers
153 views

Why are the quantum numbers $n$ and $\ell$ denoted with those letters?

We have 4 quantum numbers: principal, azimuthal, magnetic and spin (denoted $n$, $\ell$, $m$ and $s$ respectively). I assume $m$ and $s$ are simply the initials of 'magnetic' and 'spin'. Is there any ...
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0answers
128 views

Is it correct to sum over either index of the metric the same way?

I don't know if the following is correct, i want to compute the following derivative $$\frac{\partial }{\partial (\partial_{\mu}A_{\nu})}\left(\partial^{\alpha}A^{\beta}\partial_{\alpha}A_{\beta} ...
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2answers
747 views

Symbols of derivatives

What is the exact use of the symbols $\partial$, $\delta$ and $\mathrm{d}$ in derivatives in physics? How are they different and when are they used? It would be nice to get that settled once and for ...
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5answers
881 views

What is the meaning of following expression $C=\frac{\delta Q}{dT}$ mathematically?

Our professor raised the following question during our lecture in Statistical Physics (even so it's related to Thermodynamics): Many text books (even Wikipedia) writes wrong expressions (from ...
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1answer
90 views

Confusion about the Kronecker delta symbol

I am not sure I understand what the short-hand anti-symmetrization means. I.e. I know that $$\delta_{cd}^{[ab]} ~=~ \frac{1}{2}(\delta_{c}^{a}\delta_{d}^{b} - \delta_{c}^{b}\delta_{d}^{a})$$ but how ...
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1answer
62 views

How are dimensions indicated in physics equations?

The universe is often described as being 4-dimensional (having 3 spatial dimensions + the dimension of time). Some theories (such as some string theories) consider the universe as having even more ...
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61 views

Coordinate Symbol confusion in general relativity

In a previous post (Finding the metric tensor from the Einstein field equation?), the equation used lambda, rho mu and nu (not sure of the names of the letters!) for the Ricci tensor and swapped to a, ...