Relation Definition and 1000 Threads

I'm having trouble understanding some things about the De Broglie relation, λ=h/p 1. A massive system, such as an atom, is a composite of several particles (protons/neutrons, electrons), each of which is a matter wave with its own wavelength, according to De Broglie relation. But the atom...

Hello Everyone. This is my first post started on this site. Please, please, please excuse my ignorance but I couldn't seem to find the answer to my question online (although I'm sure it is). If the size of the know universe has a diameter of 93 billion lightyears with a radius in accordance to...

Hello, Can anyone explain to me why, concept wise (not from calculations that I get it), is the dispersion relation of magnons (spin waves) quadratic in k for small wavelengths? Also, can you give me other examples where such behavior appears? Thank you

I was thinking about the impact of two bodies. Let's say that we don't know the Coeffient of Elaticity. We know the mass of the object being hit "m1", the the object hitting m1, "m2". given the velocity of m2, "v", what would the force on m1 be? First let's assume that m1 is some plane or...

This question has been bugging me for a while now. I roughly understand how the Higgs mechanism gives elementary particles their rest mass and I also understand that gravity couples to all forms of energy, including binding energy in a nucleus or atom. I also know most of the mass of a system...

Hi, Just out of curiosity, why is the density and volume used to find the power of a flow of water for example. I know the equation for this is P=0.5ρAv^3 where ρ=density and v=speed of the water cubed. Any suggestions? Thank you

Hello Everyone! I have a problem I am solving through a self study project from Lowell Brown's book entitled: Quantum Field Theory". It is a math question (basically) on recursion relations. Homework Statement The variational definition gives us the relation: det[1-λK] = exp{tr...

It is kinda strange. There is no agreement on the definition of a relation. Some books says it is a set of ordered pairs. Other books says it is a subset of a cartesian product. How nice if everything can be agreed down to a few axioms like Euclid's elements. What is your favourite...

It is stated that as volumetric flow rate increses the available head decreases. Can anybody explain this sentence?

how can we prove this relation F= -dv/dx could some one explain what we mean by the force equal to the change it potential per distance and

Speed of sound at a specific temperature is independent of Pressure as Pressure varies directly with density. So wouldn't any change in density vary the pressure such that it has no net effect on speed of sound? but my book says the speed increases with decrease in density...

hi everyone, in thermodynamics, when we calculate the heat capacity in constant volume, we assume Cv=dQ/dT.. well, but at isothermal condition suddenly they came up with Cv=dU/dT... so i am getting stuck with this concept how they replace dQ with dU? i know U= internal energy is only a...

\int_0^\infty e^{-x^2}dx \int_0^\infty e^{-y^2}dy = \int_0^\infty \int_0^\infty e^{-(x^2+y^2)} dxdy Under what conditions we could do the same for other functions? I don't get how Poisson (or Euler, or Gauss, whoever that did this for the first time) realized that this is true. It looks...

I'm a fan. Not a physicist or astronomer.. But this question is bothering me. If the mass of an object increases to infinity as it approaches the speed of light, does that also create infinite gravity at the object? And if so, if we consider the gas swirling around the black hole is very...

maybe its simple permutation and combination technique... I ve tried to resolve it on my own but I couldn't...The textbook which I read simply mentions it to be obvious..can anyone please elucidate me the logic behind factorials of "independent components of tensor curl" and levi cita Can...

Homework Statement Let A = {1, 2, 3, 4} Let G = {(4,2), (4,1), (4,3), (2,1), (2,3), (1,3)} Is G a relation? is G an order relation? Homework Equations i think i should put the definitions of a relation and an order relation here. also this is from the book Elementary geometry from...

Hello everybody! I'm trying to write a car simulation but I'm having problems with precisely calculating the acceleration / velocity of the car's wheel. Currently the simulation works as if the Car was lifted in the air, so there is no load (vertical force) on the Wheel. What I have so far...

Hi all, I am preparing for a job interview in some nuclear facility and have to refresh my knowledge about nuclear stuff. So I started reading the book of Lewis "Fundamentals of reactor physics". I got stuck at page 35, formula (2.24). Does anyone have a clue how to arrive at this equation...

I was going through my basic definitions of postion (in terms of paths), velocity, and speed. The problem I am running into is this: if you can prove by definition of dot product when velocity is perpendicular to the postion function and that velocity exists, does this mean speed is...

How difficult is abstract algebra or group theory, plus complex analysis in relation to calculus?

In this Article there is a remark by biologist "It's one of the basic lessons in biology: Reproduction is very costly, and if you don't use it, you can live much longer". Can someone give few examples of species that live longer if they don't reproduce?

My book wants to find solutions to Legendre's equation: (1-x2)y'' - 2xy' 0 l(l+1)y = 0 (1) By assuming a solution of the form: y = Ʃanxn , the sum going from 0->∞ (2) Now by plugging (2) into (1) one finds: Ʃ[n(n-1)anxn-2-n(n-1)anxn - 2nanxn + l(l+1)anxn = 0...

I went back to my old introductory books on Quantum Mechanics and noticed the derivation of the de Broglie relation. Therefore I have now this question: How much does the de Broglie relation (p = hb k) depend on Special relativity? Would the dependence be strong enough that one may...

Can someone say a few words on Hubble's law as (if) it relates to QM?

Homework Statement For any quadratic polynomial ax2+bx+c having zeros β and α Prove that β + α = -b/a and αβ = c/a. Homework Equations The Attempt at a Solution I have found a method myself to prove α+ β = -b/a. However, I could not prove αβ = c/a. It goes like this. If α and β are the...

OK, so this question really digs into the heart of determinism in the realm of quantum mechanics, specifically the standard model. First let's expose my limited understanding as it exists at the moment: There are known quantities that must be conserved such as mass charge momentum etc, and...

My lecturer has said that beppo levi means for and increasing sequence of Xi where Xi is simple for all i, it holds that ∫limi → ∞XidP = limi → ∞∫XidP But why is it that he later says things like ∫ limi→ ∞ Ʃin=1P2(Bw1n)dP1(w1) = limi → ∞Ʃin=1∫P2(Bw1n)dP1(w1) is a result of beppo...

how is the quantum momentum operator (being a linear differential op.) related to commutative algebra?

Hi there, Could anybody explain how the free electron dispersion relation would be modified by the presence of a periodic potential..? I'm struggling to get my head around it. Thanks!

x_{xn-1}= 5_{xn-1} - 6_{xn-2};for \ n≥2 \\ x_{1}=1 \\ x_{0}=0 prove by induction that: \begin{bmatrix} x_{n}\\ x_{n-1} \end{bmatrix} = \begin{bmatrix} 5 &-6 \\ 1 & 0 \end{bmatrix}^{n-1}\begin{bmatrix} 1\\0 \end{bmatrix}

I assume that everyone knows the constitutive relation of dielectric material : D = ε_0E + P where D is the electric field displacement ε_0 is permittivity of vacumm E is the electric field (or may be the electric ) and P is the polarization (density*dipole) I am...

From electrodynamics we have a viewpoint about this question. From wave-particle nature in quantum mechanics,we also have a viewpoint (de Broglie' opinion).And in particle physics,we have a much higher understanding. Who can summerize the general relation between particle and field in...

dE = TdS - PdV, or equivalently \Delta E = \int T \mathrm d S - \int P \mathrm d V In general this is said to be derivable in the reversible case, however since S and V are state variables, it's also true for the irreversible case. But it can't be true for any irreversible case, since the...

dE = dQ + dW = dQrev + dWrev = dQirev + dWirev. We have for an reversible process, dQrev = TdS and dWrev = -PdV. So; dE = TdS - PdV So this relation is for all changes (irreversible or reversible) since dS and dV are state functions. What doesn't make sense to me is the next part when...

Homework Statement Assume that the distance across a microscopic cell is larger than the correlation length of the liquid, so whatever is happening in one cell is statistically uncorrelated with what is happening in an adjacent cell. Further, assume that each cell has two distinct possible...

Homework Statement Relation is x^y = y^x...x and y belong to integersHomework Equations The Attempt at a Solution Well i have already proven that they are reflexive and symmetric. I have doubt with transitive I did the follwoing way x^y = y^x...(1) and y^z = z^y...(2) from(1) x^z = y^(zx/y)...

I have this formula: (x+α)(x+α)*(y+β)(y+β)*(z+γ)(z+γ)=xx*yy*zz where α+β+γ=0 I think there might be a distance relationship between x, y and z that would satisfy the equation: if x,y and z are varied with keeping a certain measure of distance constant, the equation will be verified...

A relation R on a set S is transitive: (x, y) and (y, x) ==> (x, z), for all pairs in R So if I cannot find (y, z) for (x, y) in R, does this mean the relation is considered transitive since the condition still holds true because False ==> False/True evaluates to True? Thanks.

Homework Statement Okay, so here's the problem: (a) Let U be a universal set and suppose that X,Y\in U. Define a relation,\leq, on U by X\leq Y iff X\subseteq Y. Show that this relation is a partial order on U. (b) What problem occurs if we try to define this as a relation on the set...

A monatomic ideal gas (γ = 5/3) is contained within a perfectly insulated cylinder that is fitted with a movable piston. The initial pressure of the gas is 1.31 × 105 Pa. The piston is pushed so as to compress the gas, with the result that the Kelvin temperature doubles. What is the final...

Homework Statement Given the following recursion formula: b_{j} = 2 \frac{kj - a}{j(j+1)-l(l+1)} \cdot b_{j-1} (where a, k and l are constants) how can b_{j = l} \neq 0 if b_{j - 1} = 0. Homework Equations The Attempt at a Solution This is a part question and I really can't see why. if...

Homework Statement Find a recurrence relation for Tn, the number of ways to write an integer n as the sum of terms, each of which is 2 or 3, and the order matters. [So 2+3 and 3+2 are different sums for 5.]Homework Equations (if I had one, this would be easier) The Attempt at a Solution So I...

Hi, On a conducting planar surface, with a plane wave illuminated,(s for scattered field, i for incident field) in spherical coordinates under the tangential boundary condition that: E_{s}(\theta,\phi)=-E_{i}\theta,\phi), which is E_{s,\phi}(\theta,\phi)=-E_{i,\phi}(\theta,\phi) and...

Homework Statement show that the roots of a polynomial with real coefficients are real of form complex conjugate pairs .The inverse is not true ,in general. Homework Equations The Attempt at a Solution

I'm reading a paper on photovoltaic hydrogen production and the author claims that for reasonable solar efficiencies the band gap must be less than 2.0eV. This I understand. My question is how will it effect the photon absorption if the band gap is much smaller. Say the band gap energy is...

Can anybody clear this up for me? In his Chicago lectures in 1930, Heisenberg is quoted as saying “The uncertainty relation does not hold for the past…If the velocity of the electron is at first known, and the position then exactly measured, the position of the electron for times previous...

Hi, just wonder if anyone can help Homework Statement Apparently there is a relation between laplace transform and power series. http://www.jstor.org/stable/pdfplus/2305640.pdf?acceptTC=true states that if the discrete variable n of a power series is replaced by a continuous variable lambda...

Relation b/w slip ratio and drag force...Race car Vehicle Dynamics help... hii guyz... this is the first time i am posting on this forum and hope i ll get help... I was going through Race car vehicle dynamics by milkins and found a relation given on pg 64 which says... Drag...

Homework Statement I am on the final part of a question and I have to prove that the following is a irreflexive symmetric relation over A or if it is not then give a counter example. R is given as an irreflexive symmetric relation over A. Relation: {(X, Y) | X ⊆ A ∧ Y ⊆ A ∧ ∀x ∈ X.∀y ∈...

The relation between two terminology "cusp" (group & algebraic curve) Dear Folks: I come across the word "cusp" in two different fields and I think they are related. Could anyone specify their relationship for me?? Many thanks! the cusp of an algebraic curve: for example: (0,0)...