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56 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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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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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] ...
157 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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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 $$H=H_0+H_{int}$$...
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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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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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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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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: A(\nu,c_{1},...,c_{n}) = \sum_{mol=1}^{n} \...
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Is there a physical or mathematical symbol for “happens when”?

How would you denote symbolically, "Equilibrium happens given that ..."?
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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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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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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. ...
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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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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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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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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? ...
204 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 ...
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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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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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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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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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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!
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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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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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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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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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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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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 ...
The Lane-Emden equation is typically written as $$\frac{1}{\xi^2} \frac{d}{d\xi} \left( \xi^2 \frac{d\theta}{d\xi} \right) = -\theta^n,$$ which makes sense given the derivation on the Wikipedia page. ...