Rules Definition and 539 Threads

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...

Hello, I am newish in group theory so sorry if anything in the following is not entirely correct. In general, one can anticipate if a matrix element <i|O|j> is zero or not by seeing if O|j> shares any irreducible representation with |i>. I know how to reduce to IRs the former product but I...

Homework Statement An object of mass m=2.3±0.1kg moves at a speed of v=1.25±0.03m/s. Calculate the kinetic energy (K=1/2mv2) of the object and estimate the uncertainty δK? Homework Equations - Addition error propagation--> z = x + y and the Limit error--> δz = δx + δy -...

Given ln(ab) = b⋅ln(a) Then ln(1x) = x⋅ln(1) Also ln(2x) = x⋅ln(2) Say ln(2x) = ln(1x) Then Also x⋅ln(2) = x⋅ln(1) But, dividing both sides by x ln(2) ≠ ln(1) Similarly, x⋅ln(2) = x⋅ln(1) Dividing both sides by x and ln(2) 1 ≠ 0 But we know x = 0 as per the original statement...

My school uses Rosens book which is an awful book, would not recommend. Can anyone please help me solidify if what I am saying is true: If you are presented an argument, to even take this argument into consideration, you must prove whether the argument is valid or not. After this is done, you...

Hi, the question and Ke logic rules are attached. This is my attempt at the question. $1. P \land (R\implies Q) $ Premise $2. ( P \land Q ) \implies \lnot S) $ Premise $3. ( P \land S) \implies R) $ Premise $4. \lnot S $...

Homework Statement ## \lim x-0 \frac {xcosx-log(1+x)}{x^2}## Homework Equations ##\frac{log(1+x)}{x}=1## ...(i) The Attempt at a Solution Using (i) we can write numerator as xcosx-x, cancelling x from denominator we have cosx-1/x, this is 0/0 form so we can use LHR which gives us -sinx/1 but...

This is one of the problems I'm currently working on but understanding how to deduce the Feynman rules for this case would give me a better idea on how to do it for more general cases besides ##\phi^4## theory (which is the example commonly covered in books like Peskin and Greiner). 1. Homework...

I can't find on any good source (such as a textbook) a precise specification about the cases when Hund's rules (especially Hund's third rule) for an electronic configuration of atom are valid (the rules help to select the lowest energy state of a configuration). As far as I understood: Hund’s...

Homework Statement p→(q→r) ¬q →¬p p ----------------------- ∴r Homework EquationsThe Attempt at a Solution My book gives the following solution: (1) p - premise (2) ¬q→¬p premise (3) q, (1) and (2) and rule of detachment, (4) p and q, law of conjuctive addition . . . Can anyone explain to me...

I was wondering if anyone could point me to a set of rules for finding the base of an exponential function? I can figure out that the base of f(x)=7^x is 7 and the base of f(x)=3^{2x} is 9 but even though I know f(x)=8^{\frac{4}{3}x} has a base of 16, I don't know how that answer was reached.

Why is it that in Grotrian diagram only the 4p->3s is not allowed, but the 4s->3p, 4p-> 3d and 4d-> 3p are allowed ? I'm following the rules of Δl=±1 and Δm=0,±1 and they give the same numbers. I also tried with Δj=0,±1 and still the same. Grotrian Diagram for Hydrogen for n=[1,4]...

I've realized that a lot of textbook questions require me to google things because I have no clue how to prove certain things. For example, I do not have the fact that if the last 2 digits in a number are divisible by 4, that number is then divisible by 4. I'm pretty sure my teacher will not...

n ∑ 3 k=0 How does this make sense when k=0?

hey guys just a quick question , within the Dirac notation I we have bras and kets.Is it allowable to simply hermitianly conjugate everything , e.g: <w|c> = <b|c> - <d|c> Can we then: <c|w> = <c|b> -<c|d> Or is there some subtly hidden rule.

I was wondering how the rules work for observation in a quantum system. Particularly, about what happens if two separate entities try measuring at the same time. And also, what kinds of interactions are happening all the time that are considered measurements, for example in quantum...

How does r∪(-p∩q∩-r) simplify to r∪(-p∩q) ? The second expression is just the first with the "-r" gone at the end. I'm not seeing how to get from the first expression to the second using any of the basic laws like distribution, de morgan, tautology, etc. What am I missing?

Amateur do-it-yourself projects are enjoyed by many people. Do it yourself (DIY) is the method of building, modifying, or repairing things without the direct aid of experts or professionals. Other people sometimes enjoy helping others with projects. That is what this forum is about...

I am reading Peskin and Schroeder and finished a few years ago Srednicki. What I don't understand is why do Feynman rules work? They are supposed to represent the diverging integrals that appear in the calculations, i.e momentum integrals, are they supposed to be regarded as a pictorial...

Hi Physics Forum users. I am new here and I want to use the Mathematics part of this forum. But I am not a physicist but an economist. My questions will NOT Economics related but pure mathematical and statistical. Is it OK for me to be here then and ask questions? I am active in...

<Moderator's note: Moved from homework forum for the general question what it means. For the saddle point question, please re-post it in the homework section, but show us some effort and where you stuck.> I have been given that and that Then I am asked to show, by contradiction, that the...

Hi. I know few rules that let's me write great code: 1. "don't pollute the global namespace" when I sit down to write JavaScript code. 2. SOLID 3. KISS 4. Liskov's Open-Closed principle Can someone help me complete the list of such rules? Thanks! Have a great day!

I am taking an online course on Analytics Modeling from Georgia Tech. The introductory section included a link to a list of core Netiquette Rules, which I find pretty useful.

1. The declaration of the problem, all variables and data given / known Calculate the decay amplitude of ## \pi ^ 0 ## in an electron-positron pair ## \pi^0 \rightarrow e^+ e^- ##, assuming that the interaction is of the form ## \mathcal {L}_{int} = g \: \partial_{\mu} \phi \: \overline{\psi}...

The title, basically. I am aware of the mixing rule for the two-component form: aP = a1z12 + 2z1z2sqrt(a1a2) + a2z22 Where do I find its extension on three or more cases? SVNA does not tell anything about this.

I am going over some of my notes, and I cannot understand unions, here is the selection I am having trouble with How does the union of four different sets equal just one of the sets? Should the union of 4 sets be the four different sets instead of one. I am missing something fundamental to...

Hi educators, This may sound dumb, but my physics lecture room is our lab as well and we spend long hours in class. We spend approximately 4 hours for lecture and other activities and 2 hours for labs. Currently, I have a strict rule that only drink is allowed during lecture and other...

mod: moved from homework Does anyone know why and when this equation holds? I have searched online but cannot find the reason or the rules for the higher order derivatives.

Hi, I'm trying to compute the cross section of a gluon emission from quarks in a electron-positron annihilation at first order (I attach the diagrams below). Applying the Feynman rules the matrix element should be: My problem is that I have no idea where this minus sign comes from. (I obtain...

Homework Statement Show that the ground states for the first three elements in the “neon configuration” (Z=11 to 18) are consistent with Hunds rules. Homework Equations From Hyperphysics, the rules are: 1. The term with maximum multiplicity lies lowest in energy 2. For a given multiplicity...

Homework Statement I am attempting to solve the circuit for three currents (I1, I2, I3). I am starting with I1 in terms of I2, then using a third equation to solve for I2 in terms of E and R. I wrote my loops at the bottom of the page. I am using Loop 1 @ B, Loop 2 @ B, and Junction at B to...

Can I use Kirchoff's voltage rule to find the voltage across a charged capacitor? I don't really have a concrete.

Hello In evolution, the archetype rule is the "natural selection" rule. Are the other selection rules? (technological selection rules, cultural rules, etc) Thank you for your time. Regards, ORF

This may seem like a stupid question, but i can't get my head around this so please bear with me. I just looked at the derivation of Dirac equation and my question is: do the solutions for a free particle obey special relativity? because if yes why? I mean I thought using E2=(mc2)2+(pc)2 would...

Hi, are there people here who believe in a God? Personally I find it very funny that the arguments against a devine creator are often empirical evidence. people say that in reality it goes like this and that so there is no god.(quantum mechanics, ,special and general relativity theory and...

Consider the diagram attached for the process quark + quark -> photon + quark + quark. I want to check I have the correct expression for the amplitude for this process by using the Feynman rules. ##i,j,m,n,l,p## are colour indices. ##k## is the loop momentum. I don't care about overall factors...

Rules of Exponents (4)^(1/5) * (4)^(1/5) 4^(1/5) + (1/5) 4^(2/5) Correct? Is the answer 2^(4/5)?

Homework Statement I need to write Kirchhoff rues for the following circuit. This is not for a physics class, but for a programming class. I can do that part, but I am not sure if the equations are correct. Homework Equations The Attempt at a Solution V1-I1*R1-(I1-I2)R3-I1*R2=0...

(I am not very sure if this is a high-school level question or a undergraduate level question. Sorry.) Does our normal differentiation rules, like the product rule and quotient rule apply to vectors? Say for example, differentiate ##r \times \dot r## ##r## is radius vector, ##\dot r## is the...

Homework Statement Homework Equations V = IR P = IV The Attempt at a Solution The attempt is much too long to type out, so here is a link to a picture of my work. I'm mostly concerned about part C, because I've seen some similar problems and my answer has been different by a magnitude of 10...

Hi, What are the rules that satisfy which combination of elements are semiconductors? First one is to satisfy the octet rule to form covalent bond. This can be easily checked by looking at the group number, which is indicative of the number of valence atoms. The other is the electronegativity...

I am wondering how efficient this engine can get, I am thinking if one used a superconductive magnet that is really strong?

Homework Statement Using Hund's rules, find the ground state L, S and J of the following atoms: (a) fluorine, (b) magnesium, and (c) titanium. Homework Equations J = L + S The Attempt at a Solution I'm having trouble understanding what L, S and J mean on a basic level. I read the textbook...

I am completing a science fiction novel. The novel takes place in a universe that is twin to ours. Two children and a bitter maid--via scientific accident--were scanned and copied through a tear (created by resonance) in the membrane separating this universe and my make believe universe. In...

Homework Statement Consider a real scalar field with a derivative interaction $$\mathcal{L} = \frac{1}{2}\left((\partial\phi)^{2}-m^{2}\phi^{2}\right)+\frac{g}{2}\phi\partial^{\mu}\phi\partial_{\mu}\phi.$$ What are the momentum-space Feynman rules for this theory? Homework Equations The...

I'm taking an introductory course in QFT. During quantization of the Dirac field, my textbook gives a lot of information on how annihilation and creation operators act on vacuum, but nothing about how they act on non-vacuum states. I need these to compute $$ \int \frac{d^3 p}{(2\pi)^3} \sum_s (...

Homework Statement find the voltage between a and d and terminal of each batteries Homework Equations Junction Rule and Loop Rule The Attempt at a Solution I got three equation JR : I3 = I1+I2 LR : 45-I3-47I3-34I1 = 0 45-I3-47I3+85-I2-18I2 = 0 I can't solve these...

Consider the partition function ##Z(\lambda)## of the ##0##-dimensional scalar ##\phi^{4}## theory ##Z(\lambda)=\frac{1}{\sqrt{2\pi}}\int^{\infty}_{-\infty}d\phi\ \exp\{-\frac{1}{2}\phi^{2}-\frac{\lambda}{4!}\phi^{4}\}.## It can be shown that...

Homework Statement Determine whether the following is valid: p \rightarrow \neg q , r \rightarrow q , r, \vdash \neg p Homework Equations Modus Ponens, disjunctive syllogism, double negation. The Attempt at a Solution I've boiled it down to p \rightarrow \neg q , q, \vdash \neg p...