Rules Definition and 516 Threads

I have encountered the name "sum rules" in many places, such as EM, acoustics,... But I understand none. In what kind of situation will a sum rule occurs? What does it said exactly?

@jedishrfu posted a small summary of the main rules to a new poster. I think this is a really good idea. New posters do not read the rules and they get upset when what seems innocuous to them, is an absolute no no to PF. Cranks, trolls and the like will always be so, but the odd...

Playing Go Fish with my granddaughter. Is there a rule that says I must have a card in my hand in order to ask for it? I do not see such a rule. I can see both ways leading to problems: Suppose I must have one: I've got a hand of 3 cards, all of which are 7s. I just asked if she has any 7s...

Why does, 4√64÷2√4 =2√16 ? I can see the method (4÷2=2, √64÷√4=√16) But why is it not; 4 times √64 divided by 2 times √4 (as per BODMAS) i.e, 4 times 8 divided by 2 times 2, which = 32 Nb. When I put it into my calculator that way it gives 32 as the answer (4*√64÷2√4)

What are the rules for Vietnamese traditional wrestling? I find online sources in English that say a wrestler loses if that wrestler's back touches the ground or if both the wrestler's feet leave the ground. With that in mind, there are many videos of such wrestling online that I don't...

This thread is about whether strictly and always applying the forum rules allow for the whole picture of exact science. For every one of the rules there is a good scientific reason, the question is not about the quality of the rules but rather about the 'fruits' of applying them strictly. I...

So, I've been watching eigenchris's video series "Tensors for Beginners" on YouTube. I am currently on video 14. I am a complete beginner and just want some clarification on if I'm truly understanding the material. Basically, is everything below this correct? In summary of the derivation of the...

Hello! I have a question about selection rules and electronic transitions of a diatomic molecule: I can't find a good explanation about that, and there's so much confusion about the right rules to use. I studied that on Bransden-Joachain's "Physics of atoms and molecules", but there (to whom...

Hi, PF Got questions to start with: ¿some casual background about these Rules?; ¿are them two, as the textbook says?. https://en.wikipedia.org/wiki/L%27H%C3%B4pital%27s_rule (only one statement found) Here goes the first, from "Calculus, 7th ed, R, Adams, C. Essex" THEOREM 3 The first...

So the chain rule for second derivatives is $$ \frac {d^2 y} {d t^2} = \frac{d}{dx}(\frac {dy} {dx}) \cdot \frac {dx} {dt} \cdot \frac {dx} {dt} + \frac {dy} {dx} \cdot \frac {d^2 x} {d t^2} = \frac{d^2 y}{d x^2} \cdot (\frac {dx} {dt})^2 + \frac {dy} {dx} \cdot \frac {d^2 x} {d t^2}$$ Today I...

The LHCb collaboration at the Large Hadron Collider has developed a new set of rules for naming composite particles bound by the strong force (i.e. hadrons) that are contemplated by existing rules for naming them. This has significant practical relevance to anyone dealing with high energy hadron...

Not sure if this belongs in Chemistry or Physics. Even less sure if I understand the selection rules for electron transition correctly; hence this question. So I would be grateful for someone to please correct the following: Letting n and m be energy levels An electron that absorbs a photon...

Hi, Suppose I am given a sequence of special symbols and I want to produce the next sequence of symbols according to certain rules that transform one symbol into one or more symbols. They are 10 symbols in total, say; A, B, C, D, E, F, G, H, I, J The rules are: A transformed into B and it is...

Are the inference rules of propositional calculus tautologies ,yes or no

I already have an MSc from outside the EU. But, I also have an incomplete CS degree from Poland which I dropped out of. European Ph.D. schools often ask for a CV, not "all the transcript from all the attended programs" as they ask in North America. Therefore, can I skip the information...

Hello , we learned in thermodynamics that to calculate ΔHr °(of the reaction ) using ΔHf °(standard heat of formation ), we have to respect that ΔHf °=ΔHr ° of a reaction forming 1 mol of compound from pure elements in their most stable form at standard state . the problem is when we want to...

Hi everyone, In his book "Quantum field theory and the standard model", Schwartz derives the position-space Feynman rules starting from the Schwinger-Dyson formula (section 7.1.1). I have two questions about his derivation. 1) As a first step, he rewrites the correlation function as $$...

Several texts state the vertex HQET Feynman rule as : igTijvμ\frac{1}{1+\slashed{v}} with the reasoning for vμ presented as being due to the QCD interaction vertex being between two heavy quark propagators, which are \frac{1+\slashed{v}}{2v.k}, giving ...

really confused at this. which is rule of thumb? some slides say heuristic is rule of thumb whereas others say factual knowledge is rule of thumb. the context of this is architecture/block diagram of expert system. i think heuristic knowledge should be called rule of thumb. but i am not sure.

I'm confused by the discussion in section §30 (Parity of a state), page 98 of Landau's QM. The functions ##\psi_u## and ##\psi_g## are odd an even states respectively. If ##f## is a true scalar, then it should remain unchanged by inversion of the co-ordinates. Writing ##q' = -q##, then its...

The attached probem tricked me because the answer is apparently D and not A. Presumably because the magnetic field is weaker with 2 bar magnets joined N/S compared to a single bar magnet. So this seems to be a gap in my knowledge as to the resulting strengths of magnets joined together. Are...

Hi there. I'm trying to solve the problem mentioned above, the thing is I'm truly lost and I don't know how to start solving this problem. Sorry if I don't have a concrete attempt at a solution. How do I derive the Feynman rules for this Lagrangian? What I think happens is that in momentum...

I know lots of people here are in undergrad or graduate school (some maybe even as faculty). I'm curious how your institution is handling the return-to-school process in the midst of COVID/Delta? Are you at 100% capacity? Maybe 50% (with a hybrid online mix, for example)? Will masks and/or...

What orbitals are occupied in a synchrotron, and which selection rules limit charged particles in a synchrotron? A Schrödinger hydrogen atom is not actually the Bohr atom, but the Bohr theory gives correct energies (but not transition probabilities). Why? Because in a hydrogen-like atom, 2s...

Since the eigenvalue problem can't distinguish between a non-existent wavefunction (and therefore a non-existent particle), and the energy being zero. This is the next thing that has started bothering me on my journey to understand quantum mechanics. For example, in the algebraic derivation of...

I am taking a course on General Relativity. Recently, I was given the following homework assignment, which reads > Derive the following transformation rules for vielbein and spin connection: $$\delta e_a^\mu=(\lambda^\nu\partial_\nu e_a^\mu-e_a^\nu\partial_\nu\lambda^\mu)+\lambda_a^b e_b^\mu$$...

Digression, but what on Earth is that ruler thing he's using to calculate products at 14:10 and 15:40? Edit: I found it, it's called a "slide rule": https://www.math.utah.edu/~alfeld/sliderules/

Not sure if this is an allowed post, as it is not technically math but I'm trying to work through the below proof. If workers have a fundamental right to a job, then unemployment will be virtually nonexistent but job redundancy will become a problem. If workers have no fundamental right to a...

I am studying interacting scalar fields (from Osborn) using the path integral approach. We define the functional integral \begin{equation*} Z[J] := \int d[\phi] e^{iS[\phi] + i\int d^d x J(x) \phi(x)} \tag{1} \end{equation*} The idea is to differentiate ##Z[J]## with respect to ##J## and end...

Let us first take the S-matrix expansion (i.e. Dyson's formula) \begin{align*} S_{fi}&=\langle f | T \left\{ \exp\left( i\frac{\lambda_3}{3!}\int d^4 x :\phi \phi \phi (x) : + i\frac{\lambda_4}{4!}\int d^4 x :\phi \phi \phi \phi (x) : \right) \right\}| i \rangle \\ &= \langle f | i...

Hey! 😊 I have proven the following properties: (i) $(a\Rightarrow b)\iff (\neg b\Rightarrow \neg a)$ (ii) $[(a\Rightarrow b)\land (b\Rightarrow c)]\Rightarrow (a\Rightarrow c)$ (iii) $[a\land (a\Rightarrow b)]\Rightarrow b$ At the second part of the exercise we have to show the de Morgan...

Hey! 😊 I want to prove by using the rules of boolean algebra that the following statement is always true $$\{b\land [\neg a\Rightarrow \neg b]\} \Rightarrow a$$ Since we have to use the rules of boolean algebra, we cannot use the truth table, right? Could you give me a hint how we could...

For simplicity I only take a system of two interacting spin-##1/2## nuclei. If the spins have quantum numbers ##m_1## and ##m_2## respectively when in a certain state, then the energy of that particular state is$$E_{m_1m_2} = m_1 v_{0,1} + m_2 v_{0,2} + m_1 m_2 J_{12}$$where ##v_{0,1}## and...

I'm not very familiar with this topic so I quickly went through some introductory books on nuclear physics and read the chpater about beta decay. What I don't understand looking at this graph is the following: Why is the direct decay to ground state absolutely forbidden ? If you take a 1st order...

As per the image, I am supposed to select all the valid statements. Apparently I'm only partially correct, and so I took another look at the statements. I believe the third statement is wrong, since $$c * (a_m*a_{m+1}*a_{m+2}*...*a_n)$$ =/= $$ (c*a_m)(c*a_{m+1})(c*a_{m+2})*...*(c*a_n)$$ Thus...

Does anyone happen to know right off if it’s allowable to run a still ad (single image) for 30 seconds straight as a TV commercial in the US? I’ve never seen this. Have any of you? I tried to look it up but couldn’t find a clear answer. Not very familiar with the rules and regulations for TV...

Hey there, In QED, we often have Feynman diagrams involving various numbers of non-commuting components, such as for the one-loop vertex correction (Peskin & Schroeder, page 189): The diagram this integral corresponds to is: How do we choose which order to put the propagators and vertex...

Apologies in advance for my ignorance, I don't really have a reference to consult and Google hasn't been too helpful! In standard probability theory there are a few common useful formulae, e.g. for two events ##S## and ##T## $$P(S\cup T) = P(S) + P(T) - P(S\cap T)$$ $$P(S \cap T) = P(S) \times...

Basically the problem starts with these given premises: 1. ~ (A ∨ (B⊃T)) 2. (A ⋅ C) ∨ (W ⊃ ~D) 3. ~(P ∨ T) ⊃ D 4. ~P ≡ ~(T ⋅ S) And from these premises, I must prove ∴ ~W. This is what I have done so far: 5. (~P ⊃ ~(T ⋅ S)) ⋅ (~(T ⋅ S) ⊃ ~P) B.E. 4 6. ~P ⊃ ~(T ⋅ S)...

Summary:: Choosing the direction of the loop and the current I am attempting to work out Example 1 in the link provided. https://courses.lumenlearning.com/physics/chapter/21-3-kirchhoffs-rules/ When solving for loop aefgh, I get: I1R1-I3R3-I3r2-E2 =0 I chose the current to continue to move...

Quoting from IceCube Observatory's webpage, (Emphasis added.) The paper, available on arXiv, has been submitted to The Astrophysical Journal. I haven't read through the paper yet, but if this detection cannot be explained by the Standard Model, what could possibly be the cause? Is there any...

Hi, I am havinga bit of challenge with the following question. What seems confusing to me is th relationship between hypothesis 1 and 2. I will appreciate all help.

I suppose my question is, since X commutes for H, does this mean that the selection rules are $$<n',l',m'|X|n,l,m>=0$$ unless $$l'=l\pm 1$$ and $$m'=m\pm 1$$, as specified in Shankar?

Please prove the rules of significant figures. I do not know why when multiplying and dividing we have to retain the same number of significant figures as in the number with the least of them.

So as I can see from the literature there are two "methods" on how to apply Hund's rules to determine the ground state of an electron configuration. Method 1: One determines all possible states due to Pauli's principle (wave function must be totally antisymmetric) using angular momentum...

I am a free-lance Software developer. Recently, I got a big project in my very 2nd assignment where I need to develop a Vibration Analysis Software for condition monitoring of some heavy motors. One of the "Terms & Conditions" of the project is that there must be at least 200 pre-definded...

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(A)My textbook states the following : (1) The example explaining the italicised statement is rather confusing. My understanding of the statement is that we need to include one extra significant figure than what the relevant rule requires us to round off to, for intermediate...

Two questions, where the 1st is related to previous discussion regarding thes couplings: The selection rules for LS coupling is quite clear - it's based on calculating the compatible electric dipole matrix element. However, in the case of jj coupling we end up with different selection rules...

When viewing an HR diagram, the main sequence curve is apparent, and the general shape of it is obvious. However, in this truncated version, it's unclear to me exactly which stars should be considered main sequence. I've added a shaded grey area as what I think I should count as main sequence...