Recent content by ian2012

Okay, i may have canceled abit too early, the factorization I am looking for is of: (E - lamda - a)^2(E- lamda + a) = a(E - lamda - a)

Yeah, i know the solutions , thanks... Well i end up with (E - lamda - a)(E - lamda) + a(E - lamda - a) - a = 0 as the equation of the determinant. I am a bit rusty on my high school algebra, is there a way to factorise that? (You could multiply it all out and spend a lifetime dividing it by a...

Hope someone can help me out here.. I've found the eigenvalues (lamda) of this matrix, but through a very very long way, does anyone know of a quicker way (there must be a quicker way). The matrix is 3x3: H = ( E, a, a; a, E, a; a, a, E ). I can reduce the determinant to the following, but...

Oh right, of course, so it let's you simplify the expression.

I hope someone can help me out here, I am confused with a line of text I read - it is an example of a 2D Hilbert space with orthonormal basis e1, e2. The Hamiltonian of the system is the Pauli matrix in the y-direction. Given by the matrix: \sigma_{y} = (\frac{0, -i}{i, 0}) The eigenvectors...

Yeah, the property is overlooked on many sites I have been on. However, I looked in Dirac's Principles of QM and he explains it there, which is fantastic. But it's a quite basic property of linear operators you can infer from simple derivatives.

Oh sorry, I understand what i did wrong. Is it right to say: (A(hat) + B(hat)).|psi> = A(hat)|psi> + B(hat)|psi> ? If so, then I believe that is the condition I was looking for... Well.. it has to be correct as it works for replacing the operator with real numbers.

What linearity condition do you use ?

Thanks for all of your posts. I have, since, extensively been reading about Dirac notation, dual space, projectors, etc.. but I still have one query regarding an operation with commutators. How do you go from: <x'|x(hat)A(hat) - A(hat)x(hat)|x> to x'<x'|A(hat)|x> - <x'|A(hat)|x>x ? (You may...

Do you know of a website or (intuitive) method i can use to learn the properties of bra-ket algebra? How did you learn it, for instance?

Okay, I didn't know you can multiply it from both sides. I know that A is a matrix, but the bra's and ket's are just vectors.. and i know that the matrix A can be found using the orthonormal basis, but i can't seem to make sense of it.

I have a basic question that I have overlooked in the past, given that you have <psi2|A = lamda2<psi2|, where <| is a bra and lamda2 is the eigenvalue. If you were to multiply the equation by |psi1>, why do you get <psi2|A|psi1> = lamda2<psi2|psi1> and not |psi1><psi2|A = lamda2|psi1><psi2| ...

I was just looking at an expression (a dispersion relation, omega^2 = ...) similar to that of warm electron's in a plasma http://en.wikipedia.org/wiki/Plasma_oscillation expect with an extra imaginary term, which I think comes out from the full derivation of the dispersion relation for warm...

Okay then, so weak interactions don't really proceed at low energies? (i am not too sure what the ideal energies are for strong interactions).

I just read something about the creation of deuteron in the first step of the pp cycle. Given that you have the reaction: p + p -> d + e^+ + v_e, where e^+ is a positron and v_e is an electron neutrino. Since there is a neutrino present, it is a weak interaction. In addition, as the interaction...