Relation Definition and 1000 Threads

Hello! (Wave) Could you explain me why the following stands? (Thinking) If $R$ is a relation, then: $$R \subset dom R \times rng R \subset fld R \times fld R$$

I am learning some basic solid state physics idea, like density of state ...etc. For particle in a 1D box, E = n^2 (pi)^2 (h_bar)^2 / 2mL^2 But why it is written as E = (h_bar)^2 k^2 /2m does it means that energy eigenvalue E is related to momentum k ? I guess it is not because momentum is...

As we know \ a= \frac {F} {m} So does this equation prove that acceleration is directly proportional to the net force and inversely proportional to the mass of the object?

Hello! (Wave) I want to use the master theorem, in order to find the exact asymptotic solution of $S(m)=4S \left ( \frac{m}{2}\right )+m^3 \sqrt{m}$. $$a=4 \geq 1, b=2>1, f(m)=m^3 \sqrt{m}$$ $$m^{\log_b a}=m^{\log_2{2^2}}=m^2$$ $$f(m)=m^{3+\frac{1}{2}}=m^{\log_b a+ \frac{3}{2}}$$ Thus...

Technically I'm supposed to have a total of 8 optical modes but only 4 of them were seen in a solid (by spectroscopy). So I suspect there's some degeneracies and symmetries involved, but I don't know which ones. I have two sets of assigned degeneracies: frequency; degeneracy set 1; degeneracy...

what's the relation of the viscous hydrodynamic forces and swirl？

I know that the matrices {\Gamma^{A}} obey the trace orthogonality relation Tr(\Gamma^{A}\Gamma_{B})=2^{m}\delta^{A}_{B} In order to show that a matrix M can be expanded in the basis \Gamma^{A} in the following way M=\sum_{A}m_{A}\Gamma^{A} m_{A}=\frac{1}{2^{m}}Tr(M\Gamma_{A}) is it enough to...

Hello! (Wave) I want to prove that $T(n)=4 T \left ( \frac{n}{2}\right )+n^2 \lg n=O(n^2 \lg^2 n)$,where $T(n)$ is constant for $n \leq 8$, using the following method: "We choose a specific function $f(n)$ and we try to show that for an appropriate $c>0$ and an appropriate $n_0 \in...

Hello! (Wave) I want to find an asymptotic upper bound for the recurrence relation: $T(n)=9T \left (\frac{n}{3} \right ) + n^2 \log n $, $T(n)=c, \text{ when } n \leq 9$, using the following method: We choose a specific function $f(n)$ and we try to show that for an appropriate $c>0$ and an...

Hi! I understand that if you have a stator with a a three phase electric signal going into it, both the frqyency and angular velocity of the magnetic field and the electric entry will be the same. Now when you feed it with 2 groups of three phases electric signals you get four poles, or at least...

What method should i use to know if a recurrence relation is increasing or decreasing? i was given the following relation: A1 = 1 An=(An-1)^5 - 3 I know for sure it actually decreases since every term for n>=2 is a negative number raised to and odd number, but i don't know how to demonstrate...

Hi! (Wave) Let $R$ be a relation. Show the following sentences: $dom(R^{-1})=rng(R)$ $rng(R^{-1})=dom(R)$ $fld(R^{-1})=fld(R)$ $(R^{-1})^{-1}=R$ That's what I have tried: Let $x \in dom(R^{-1})$. Then $\exists y$ such that $<x,y> \in R^{-1} \Rightarrow <y,x> \in R \Rightarrow x \in...

1. The problem I am trying to prove the following relation in cartesian coordinates. We were given a hint to use integration by parts, as well as the fact that we know $d \vec r = dx\,dy\,dz$ (volume integral). $$\int f(\vec r)\ \nabla \cdot \vec A(\vec r) \, d \vec r = -\int \vec A(\vec...

Hey! (Cool) According to my notes, each relation is a subset of an ordered pair. How can it be that each relation is a subset of an ordered pair, knowing that a relation is a set of ordered pairs? (Thinking)

Hi Physics Forums, The solubility of a gas according to Henry's Law depends on partial pressure. Would an increase in pressure in a system increase the solubility of a specific gas, even if the partial pressure of that particular gas doesn't change? The system described above increases in...

Homework Statement Calculate the commutator ##[\hat{L}_i, (\mathbf{rp})^2]## Homework Equations ##\hat{\vec{L}} = \sum\limits_{a=1}^N \vec{r}_a \times \hat{\vec{p}}## ##[r_i,p_k] = i\hbar\delta_{ik}## The Attempt at a Solution Okay so here is what I have so far: $$ \begin{eqnarray}...

Hello! (Wave) I want to prove by induction, that the solution of the recurrence relation $T(n)=2T \left ( \frac{n}{2} \right )+n^2, n>1 \text{ and } T(1)=1$ is $n(2n-1)$. We have to suppose that $n=2^k, k \geq 0$, right? Do I have to prove the solution by induction with respect to $n$ or to...

Homework Statement [/B] A particle of mass m is moving in the +x-direction with speed u and has momentum p and energy E in the frame S. (a) If S' is moving at speed v, find the momentum p' and energy E' in the S' frame. (b) Note that E' \neq E and p' \neq p, but show that...

I'm in calc 1 and want to make sure I'm understanding the reason that we find derivatives. From what I understand, a derivative is simply an equation for the rate of change at any given point on the original function. Is that correct? And the tangent line at point (x,y) is obtained by using...

I am given a formula in explicit form and as a recurrence relation. It is asked to derive the recurrence relation from the explicit form. How is this done?

Hey again! (Wave) I have to determine if $g(n)=O(g^5(n))$ is true or not. I thought that I could use the definition of Big-0h, but I don't know how to begin, formulating it. From the definition, we have that $\exists c>0$ and $n_0 \in \mathbb{N}_0$ such that $\forall n \geq n_0$: $$0 \leq...

An observer in an inertial frame finds that at a point P the Electric field vanishes but the Magnetic field does not. This implies that in any other inertial frame the electric field E and the magnetic field B satisfy: [these values in vectors] 1. |E|2 = |B|2 2. E . B = 0 3. E x B = 0 4. E = 0...

Hello all, this is my first post! Hopefully I can gain some valuable insight. Homework Statement Find the relation among T, P and mu for the system with the given equation U = b S4/NV2 I let b equal the several constants stated in the problem. Homework Equations T=dU/dS P=-dU/dV mu=dU/dN The...

Let $U_1,\,U_2,\,\cdots$ be a sequence defined by $U_1=1$ and for $n>1$, $U_{n+1}=\sqrt{U_n^2-2U_n+3}+1$. Find $U_{513}$.

Homework Statement I've determined the dispersion relation for a particular traveling wave and have found that it contains both a real and an imaginary part. So, I let k=\alpha+i\beta and solved for \alpha and \beta I found that there are \pm signs in the solutions for both \alpha and \beta...

Hello! (Cool) Sentence The set, that does not contain any element, is unique. Proof: Let's suppose that $a,b$ are sets, so that each of these sets does not contain any element and $a \neq b$. From the axiom: Two sets, that have the same elements, are equal., there is (without loss of...

Homework Statement I have a homework problem in honors calculus III that I'm having a little trouble with. Given these three qualities of norms in Rn: 1) f(v)\geq0, with equality iff v=0 2) f(av)=|a|f(v) for any scalar a 3) f(v+w) \leq f(v)+f(w) we were given a set of 3 functions and told...

Homework Statement Differential equation: 2xyy' = x^2 + y^2 Relation: y^2 = x^2 - cx Homework Equations The Attempt at a Solution Hello, I can normally solve this problems with ease; however, I am having trouble with this particular problem. I have performed the implicit...

Hello, it is known that given a certain recurrence relation that describes a sequence of numbers, it is often possible to obtain a function f[n] that directly yields the n-th number of the sequence. This is usually accomplished by using powerful techniques involving generating functions or the...

When waves are propagated through medium, the displacement curve will move up and down. Do they have any relationship with propagated energy? For example, when energy is gained from other part the curve will rise up or fall down. And does energy in standing waves share similar principle?

I'm new to the concepts of quanum mechanics and the bra-ket representation in general. I've seen in the textbook that the compleatness relation is used all the time when working with the bra and kets. I'm a bit confused about how this relation is being used when applied more than once in a...

Dear all, If I have the value of photosynthetic photon flux in unit [ micro mole per meter square per second] as an output for ultra violet sensor. How can I know the corresponding wavelength of that radiation ? and can I know from that wavelength what is the type of the ultraviolet...

http://arxiv.org/abs/1409.0492 Is the Standard Model saved asymptotically by conformal symmetry? A.Gorsky, A.Mironov, A.Morozov, T.N.Tomaras (Submitted on 1 Sep 2014) It is pointed out that the top-quark and Higgs masses and the Higgs VEV satisfy with great accuracy the relations...

Hi ALL, On this forum, I found some really sensible answers to a few of my queries... posting one that's unanswered.. I want to understand how an engine or any power plant for that matter behaves under load... So I'm using a simple scenario to frame my questions... the values while made up...

Homework Statement The spin 1/2 electrons are placed in a one-dimensional harmonic oscillator potential of angular frequency ω. If a measurement of $$S_z$$ of the system returns $$\hbar$$. What is the smallest possible energy of the system? Homework Equations...

After being through with Newton's 3rd law of action reaction pairs, there arise a doubt regarding the categorization of force couple (related to torque) of being or NOT being an example of action reaction pairs.

Hi, what is the physics experiment that leads to the position-momentum commutation relation xpx - px x = i hbar What does it mean to multiply the position and momentum operators of a particle? What is the corresponding physical quantity?

I don't understand why we quantize the field by defining the commutation relation.What's that mean?And what's the difference between the commutation and anticommtation?

Hello, I read the Feynman's QED book, where I learned that a photon has a intrinsic property called frequency. This property affect, for example, the interference profile when we have a lot of photon together. Ok. Now, thinking on an conventional antenna. When we have a 100kHz signal on...

Homework Statement Greetings! I am reading section 2.8 of Jackson and trying to understand how completeness relation was derived. It starts with the orthonormality condition: ∫U_N ^*(ε) U(ε) dε =δ_{nm} We can represent a function as a sum of orthonormal functions if N is finite...

Hello everyone, this has been on my mind for a while and I finally realized I could just ask on here for some input :) I think in general, when most people start learning quantum mechanics, they are under the impression that the wave function \Psi represents everything you could possibly know...

Show that for $|a| > |b| $, $$\int_{0}^{\infty} \frac{\sinh bx}{\cosh ax + \cosh bx} \ dx = 2 \ln 2 \ \frac{b}{a^{2}-b^{2}} .$$

[SIZE="4"]Definition/Summary One of the most asked questions is concerning how to derive the Heisenberg Uncertainty Relation. Starting from almost basic concepts of Quantum Mechanics, a derivation is given here. Some details are left as minor exercises for the interested reader. The...

[SIZE="4"]Definition/Summary A recurrence relation is an equation which defines each term of a sequence as a function of preceding terms. The most well-known are those defining the Fibonacci numbers and the binomial coefficients. An ordinary differential equation can be considered as a...

[SIZE="4"]Definition/Summary A relation on a set A is a set of ordered pairs (a,b) of elements ofA (a subset of A \times A). An equivalence relation \sim\ \subseteq A \times A is a relation which is reflexive, symmetric and transitive. In other words, the relation \sim on A is an...

Hi guys, I am still new to this forum, so I hope I can learn many things from this forum :) I am currently looking for my IB EE topic about the relation between temperature and natural frequency on an object. I have been researching about this topic, however I don't find any specific...

I'm having a brain fart so this is just another silly question but... when deriving the I-V relation for the capacitor: $$C=\frac{dq}{dV}$$ $$\frac{d}{dt}C=\frac{d}{dt} (\frac{dq}{dV})=\frac{d}{dt}C=\frac{di}{dV}$$ from here, normally we're supposed to do the following...

Hello! (Wave) I have to define an asymptotic upper and lower bound of the recursive relation $T(n)=5 T(\frac{n}{5})+\frac{n}{ \lg n}$. I thought that I could use the master theorem,since the recursive relation is of the form $T(n)=aT(\frac{n}{b})+f(n)$ $$a=5 \geq 1 , b=5>1 , f(n)=\frac{n}{...

Using the Hall-Petch relation, estimate the yield strength, σy, of a Cu-Zn alloy (brass) when the average grain diameter is 30 μm. where: σy = is the yield strength σ0 = 25 MPa is the internal friction stress ky = 12.5 MPa·mm1/2 is a material constant d = is the average grain size...

Is there a formal relation that links \int yxdx OR \int_{a}^{b}yxdx with \int xydy OR \int_{a}^{b}xydy where y=f(x) over the interval x\in\left[a,b\right].