Rules Definition and 539 Threads

Homework Statement 2. Evaluate the determinants ## \begin{vmatrix} 1 & 1 & 1\\ x & a & b \\ x^2 & a^2 & b^2 \\ \end{vmatrix} ## ## \begin{vmatrix} x & a & b \\ x^2 & a^2 & b^2 \\ x^3 & a^3 & b^3 \\ \end{vmatrix} ## and factorize both answers. Homework Equations Rules of determinants are...

Hi guys, I'm assume that you already know the 7 crystal system, each crystals have unique way of determining the family of planes, for example in cubic, we all know (111) plane is same (-1-1-1), and so on ((-1-11),(-11-1)...) a total of 8, in fact there is pattern to determine how many possible...

I have attached the properties/rules that will aid in simplifying the 3 x 3 determinant so that it can be calculated with minimum effort. I am trying to understand rule (2) and (4). I am not so clear about the idea of linearity. Can anyone please explain these two rules with regards to example...

Are there any generally accepted techniques for maximizing cell phone reception with regards to phone orientation? When I search for this question on Google I get "answers" that seem more opinion than anything. Any engineers in the house with definitive experience with this topic and confident...

When we first learn of selection rules for atomic transitions, we learn that electrons have to change between states that differ in angular momentum by at most 1ħ, because photons have 1 unit of spin angular momentum. However, photons can have arbitrarily high integer quantities of orbital...

Homework Statement Consider the following real scalar field in two dimensions: S = \int d^2 x ( \frac{1}{2} \partial_\mu \phi \partial^\mu \phi - \frac{1}{2} m^2 \phi^2 - g \phi^3) What are the Feynman rules for calculating < \Omega | T(\phi_1 ... \phi_n ) | \Omega > 2. Homework...

I'm trying to learn how to derive Feynman rules (what else to do during xmas, lol). The book I'm using is QFT 2nd ed by Mandl&Shaw. On p 428 they're trying to show how to derive a Feynman rule for W W^\dagger Z^2 interaction term g^2 \cos^2\theta_W\left[W_\alpha W_\beta^\dagger Z^\alpha Z^\beta...

Suppose we define the total angular momentum as F = I+J where I is the nuclear spin angular momentum and J is the total electronic angular momentum. mF and mJ are the respective magnetic quantum numbers. The relevant F selection rules are delta_mF = 0, 1 and -1, delta_F = 0, 1 and -1. And...

My instructor was talking about allowed transitions for IR spectroscopy and how you can predict them relatively well using PIB wavefunctions. It was stated that you could solve for the probability of a transition moment to determine if a transition is forbidden or not. <μ>=∫ΨfμΨidτ...

(I have posted this in this section, rather than homework, because I hope to improve my general understanding of methods of finding limits through these problems.) 1: \lim_{x\rightarrow0} (\frac{cosec(x)}{x^3} - \frac{sinh(x)}{x^5}) I don't really know what to do with this one. I tried...

Homework Statement This is more of a general question-- as the title suggests I'm not too sure how to place the terms given by the Feynman rules for fermions (since they involve operators and spinors, the order does of course matter). I've been reading Peskin & Schroeder and the rules are...

Hi Guys and Grillz Im not sure how these forums work, but if someone could help me real quick by explaining me how i should count this (3x2y)^8 (2xy)^3. I am sorry if i asked a dumb question or posted it in the wrong place. This is my first time doing this. :D

For an atom, the single photon electric dipole selection rules for the magnetic quantum number require that delta_m = -1, 0 or +1. As I understand, the physical explanation for this set of selection rules is usually related to the conservation of the projection of the angular momentum on the...

I'm a little confused by the description I commonly hear about the electron "counting rule" in band theory. The general statement I find is that a solid with an "odd number of electrons per unit cell is a metal" (because this would imply a partially filled band), while an "even number of...

Consider the circuit shown in the figure . Suppose the four resistors in this circuit have the values R1 = 12 , R2 = 6.0 , R3 = 7.3 , and R4 = 15 , and that the emf of the battery is E = 18V . (1) Find the current through each resistor using the rules for series and parallel resistors. Answer...

Homework Statement Use the Bohr quantization rules to calculate the energy levels for a particle moving in a potential \begin{equation} V\left(r\right)= V_0 \left(\frac{r}{a}\right)^k \end{equation} where k is positive and very large. Sketch the form of the potential (done) and show that the...

Consider the electric circuit shown in the figure. Using Kirchhoff's rules, select True or False for the following equations. a.) I2 + I3 = I1 b.) ε1 - I2R2 - I3R3 - I1R1 = 0 c.) ε2 - I1R5 - I3R3 - I2R4 = 0 http://tinypic.com/r/2zyws55/8 My answers were: True, False, False. However, the...

Homework Statement A exp( (− 3 R^2)/(2Na^2)) I wish to integrate ^ The expression is equal to P(N,R) The limits are infinity to -infinity. The intention is to find the normalisation constant / A in terms of N and a (then to cube it).The Attempt at a Solution This is what I've managed. A S...

Hi, Are there any rules against multiplying or adding first when using modulo #? The reason I ask is because I'm doing the dot product for two vectors: [10, 9, 8, 7, 6, 5, 4, 3, 2, 1].[8, 0 ,3 ,7, 0, 9, 9, 0, 2, 6] By doing this, I get: 80 + 0 + 24 + 49 + 0 + 45 + 36+ 0 + 4 + 6 =...

Source: the website of University of Toronto's The Ontario Institute for Studies in Education, http://fcis.oise.utoronto.ca/~daniel_sch/assignment1/1915rules.html

Homework Statement http://imgur.com/XXPWbCN Homework Equations ∑ ΔV (closed circuit) = 0 ∑ I (in) = ∑ I (out) The Attempt at a Solution So I know that the sum of the currents entering any junction in a circuit must equal the sum of the currents leaving that junction, and that the...

Hello, I thought I had questions concerning Kirchoff's rules down to a tee, but now capacitors have entered the scene and I'm stumped. Homework Statement The circuit in the drawing (attached) shows two resistors, a capacitor, and a battery. When the capacitor is fully charged, what is...

Hi, My textbook is giving me 3 rules that must be met to be continuous: I don't understand what my textbook is trying to explain to me, - ƒ is defined at a...:confused: -Lim ƒ(x) = ƒ(a)...:confused: x→a all i undersdand is that if you draw a graph that is continuous, you must be...

Homework Statement Consider the following statements. All engineers either like computer or like power tools. All engineers who like computers like video games. All engineers who like power tools like camping out. Some engineers like literature. Based on these given statements, show that...

Hi, i'm stuck on this problem and have been trying to identify where I might have made an error but have come up empty. I have assigned my loops and junctions and have three equation for three unknowns, but can't seem to solve them... Homework Statement Consider the circuit in the...

Homework Statement If R1 is 3Ω, R2 is 6Ω and R3 is 9Ω, what are the three currents in figure 16-4, in which the batteries are 6.0v and 12.0v? Homework Equations I1+I2+I3 The Attempt at a Solution I've got three equations so far I worked out +6-3I1-9I2=0 and...

I have two related questions to ask relating to statements found in introductory particle physics textbooks. The first is that the "Dirac equation predicts fermions/anti-fermions have opposite intrinsic parity". I have attempted to verify this by applying the parity transformation to free...

Val[a_] := ToCharacterCode[ToString[a]][[1]]; GH[a].GH[b].GH[c].GH[d].GH[b] //. {GH[a_].GH[b_] :> If[Val[a] > Val[b], GH[b].GH[a], GH[a].GH[b]]} I have the noncommutative multiply of GH[a].GH[b].GH[c].GH[d].GH[b] My goal is to order these in increasing charcter value. (Val is the function...

Dear every specialists, I heard that BICEP2's observation r=A_t/A_s=0.2 n_t=0 indicate two things: 1) n_t=0 excludes ekpyrotic cosmological model (ECM) definitely because ECM predicts n_t=2 2) r=0.2 excludes almost all current string inflation model (SIM) such as KKLMMT because this...

Honestly, I do not really understand how to apply rules of inference. So i would appreciate if u could explain without missing any point. I think i got this, is this the correct answer? Pls refer to image.

Homework Statement Is it true that: (ABA^-1)^8 = AB^8A^-1 for all n x n matrix and not just for invertible matrix? My attempt: (ABA^-1)^8 =A^8B^8A^-8

Hi everyone, This is a question about conformal field theory. Even though it is not directly about beyond the SM, it seems like an appropriate place to ask since it is an important tool in string theory. I am confused by the fusion rules \phi_i ~ \phi_j = N^k_{ij} \phi_k (where as...

When can you use this formula? On page 13 it uses it here: http://web.mit.edu/8.02t/www/802TEAL3D/visualizations/coursenotes/modules/guide06.pdf however my instructor said that you can only use it when you are using a wire and the current is flowing parallel to the axis.

Problem statement Find dy/dx Revelant equations None Attempt at a solution This is what I got to so far but now I'm stuck... Any hints?

Homework Statement I need to come up with a formula to solve for i2 given the diagram of the circuit attached. I can identify 2 junctions and 3 loops. Homework Equations *The algebraic sum of the currents into any junction is 0. By convention the currents entering the junction are positive...

The attached picture shows a representation of a general operator, which I found quite weird. The matrix elements are calculated in the position basis as far as I can tell, but I am not sure how. Do they do something like? <klTlk'> = ∫ dx dx' <klx><xlTlx'><x'lk'> In that case what happens to...

Are there "road" traffic rules in Space? Do you have to "stick to the left of your orbit" or "give way to the unmanned vessel"?

problem is solved.

Hi, I'm looking get a deeper conceptual grip on A&M spectroscopy, particularly what actually goes on between atoms/molecules and photons during an emission/absorption event. In general I just want to understand the "why's and how's" of the selection rules for dipole/quadrupole transitions, but...

I learned this a while ago in my calculus 2 class and I was just thinking about it... Where do these error equations for each of the approximation rules come from? Like for example, where does the error for the Simpson's rule, $$|E_{S}|\le \frac{M(b-a)^{5}}{180n^{4}}$$ come from? Also, why even...

Hi all, The context of this problem is as follows: I'm trying to implement a discontinuous finite element method and the formulation calls for the computation of line integrals over the edges of the mesh. Anyway, more generally, I need to evaluate \int_{e}f(x,y)ds, where e is a line segment...

Homework Statement Find the gradient of the curve at the given point on the curve y = \frac{(√x - 1)}{√x} where x = 9 Homework Equations y(x) = u(x)v(x) dy/dx = u(dv/dx) + v(du/dx) The Attempt at a Solution my problem really boils down to rearranging the function to a form...

Hi, I've read somewhere that the Quantum Zeno effect, should it really exist, rules out the many-worlds interpretation. However I did not understand the argument (actually there was no argument, seems the author considered it obvious). Could someone please elaborate on this? BTW, what's...

In addition to the Global Guidelines, these rules also apply to posts in the lounge. Overly Speculative Posts It is against our Posting Guidelines to discuss new or non-mainstream theories or ideas that have not been published in professional peer-reviewed journals or are not part of current...

Here is the question: I have posted a link there to this topic so the OP can see my work.

Homework Statement Find Kirchoff's laws for this http://postimg.org/image/d78dvdg5f/ (Actual problem has a bit more but I can do that part.)Homework Equations Loop rule Junction ruleThe Attempt at a Solution I got the following equations 2e - 4i_4 - 2i_2 = 0 e - 3i_3 - i_1 = 0 e - 4i_4 -...

I was just reading that because of superselection rules we cannot superpose two particles with different electric charges. But when I look in my particles physics books it seems there are decay processes that do this all the time: consider \pi^+ → μ^+ +\nu_\mu , for example. Can anyone tell me...

Homework Statement What are the sizes and directions of the currents through resistors (a) R2 and (b) R3 in Fig. 27-42, where each of the three resistances is 4.0 Ω? Homework Equations ΔV=IR The Attempt at a Solution Equations: 1) ΔVB2 -(i1)R1 -(i2)R2 -ΔVB1=0 5V - 4(i1)...

I am having a little trouble remembering the rules with derivatives. $\frac{a}{1-r}$ I know that it should be (derivative of the top*bottom - top*derivative bottom) / (bottom squared). $\frac{d}{dr}\frac{a}{1-r}$ I tried this got the answer wrong, and looked up how to do this and they showed...

Hello everyone, I am a bit confused about definitions rules. I can have more questions but for now I want to ask only one question: Let us say I have a number: \sqrt[6]{3x3x3x3x3x3} 3x3x3x3x3x3 is equal to both 27^2 and (-27)^2. But If I write these two expressions separately I can get...