Recent content by Rettaw

Well, actually "elementary algebra" wasn't that helpful. But thinking to myself about how to explain why it wasn't helpful WAS helpful, so thanks for the help :) Anyway, for completeness and posterity this is (my guess at) the solution: Starting with 3 H^2 - c^2 \Lambda = \frac{8 \pi...

Hello, I am reading this paper about quantum gravity, trying and failing to follow along in the derivation of this, eq (204) p. 72, expression for the scale factor: a(t) = a_1 \left( 1 + \frac 3 2 ( 1 + \omega ) H_1 (t - t_1) \right)^{\frac 2 {3(1+\omega)}} (I'm not sure what the...

Yeah, you're right it's supposed to be only a^{\dagger} and no powers of n. Still, I'm not entirely convinced, the \left[ a , a^{\dagger} \right] is indeed a c-number, but the \left[ a^m , a^{\dagger} \right] is an operator, and when I expand the full \left[ a^m , (a^{\dagger})^n \right]...

Besides direct integration I'd suggest you look at the greens function for the Poisson equation.

You don't really calculate them, maybe you mean why did Pauli construct them? As I recall it they where constructed to have the properties of the angular momentum algebra, that is (up to constants I can never recall) [\sigma_i , \sigma_j] = \epsilon_{i,j,k}\sigma_k where the epsilon...

Hello, I have the missfortune of having to calculate a commutator with some powers of the creation and the annihilation operators, something like: \left[ a^m , (a^{\dagger})^n \right] I have managed to derive \left[ a^m , (a^{\dagger})^n \right]= m a^{m-1} \left[ a , a^{\dagger}...