Recent content by Repetit

My math book claims that the piecewise function f : [0,1] U (2,3] --> R defined by f(x)= x for 0<=x<=1 x-1 for 2<x<=3 is continuous. But it's undefined for 1<x<=2 so how can it be continuous? According to the definition of continuity, a function is at a point x0 if for a sequence x_n...

Homework Statement Prove that the sequence {c_n} converges to c if and only if the sequence {c_n - c} converges to zero. Homework Equations The Attempt at a Solution First I prove that the convergence of {c_n - c} to zero implies that {c_n} converges to c by (all limits take n to...

Hey! I need to perform the following integration: \int\limits_0^{\infty} J_1(k r)k dk where J_1(x) is the cylindrical Bessel function of the first kind. This is an oscillatory function with amplitude decreasing as 1/\sqrt{x}. Due to the multiplication of k the integrand however, becomes...

Hey. Is the conductivity of a material related to the dielectric constant (permittivity) in some way? And what about the electrical susceptibility? Thanks

Thanks for the answers. I think the definition the book gives of equality between sets, is that for two sets A and B to be equal, A must be a subset of B and B must be a subset of A.

Hey Im trying to study abstract algebra, set theory and group theory, on my own. I have trouble understanding how to construct mathematical proofs though. Some of the things the excercises tells me to prove, seems so intuitively clear and obvious that I don't know what's left to prove. For...

Thank you for the answers! It makes more sense to me now.

In a semiconductor the law of mass action states that the product of the electron concentration and the hole concentration is always equal to the square of the intrinsic carrier concentration (at a given temperature), i.e.: n p = n_i^2 My book states that this law is valid for...

That makes sense to me... Thank you. :) And yes, I am talking about energy levels for multielectron atoms in the Russel-Saunder coupling scheme. But, what I am basically trying to do is to calculate the energy of excited states of some atoms without the effect of spin-orbit. Now, let's say I...

Thanks for the reply! But, in an f-shell with 3 electrons for instance, even if we assume that the 3 electrons all have spin up we still get several atomic terms. How can that be, what degrees of freedom are left when the configuration is locked and the spins of the electron is also locked. The...

Can someone explain to me why different terms arising from a particular electron configuration have different energies? For example, for carbon in the configuration 1s^22s^22p^2 three terms arise, 3P 1D and 1S. These three terms have different energies but I don't understand why. The electron...

When calculating eigenstates in the hydrogen atom one finds plenty of eigenstates with angular dependence. The s orbitals are spherically symmetric, but an orbital like 2p is not, there is some angular dependence through the spherical harmonics. But why is there angular dependence? It is a...

Hey! Could someone please help me find out how to express the product of two Legendre polynomials in terms of a sum of Legendre polynomials. I believe I have to use the recursion formula (l+1)P_{l+1}(x)-(2l+1) x P_l(x) + l P_{l-1}(x)=0 but I am not sure how to do this. What is basically...

Light in a vacuum has momentum \hbar k but when the light enters a dielectric medium, fx. glass, the momentum of the light is increased to \hbar\sqrt{\epsilon} k, where \epsilon is the dielectric constant of the dielectric. Where does the extra momentum come from? How can this be in accordance...

Hmm, I see, that makes sense. Thanks to both of you!