Recent content by David932

1. Problem statement : suppose we have a Hermitian 3 x 3 Matrix A and X is any non-zero column vector. If X(dagger) A X > 0 then it implies that determinant (A) > 0. I tried to prove this statement and my attempt is attached as an image. Please can anyone guide me in a step by step way to...

Thanks for the reply. Yes, I should take the square root at the end.

My question is whether the formula I used and the answer I got is correct or my logic has a conceptual mistake?

Hi BvU i edited my question and included the formula which I used for getting the answer.

Homework Statement Let a is a complex vector given by a = 2π K - i ρ / α^2 , where ρ is a two dimensional position vector and K is the corresponding two dimensional vector in the Fourier space. In order to find magnitude of this vector, i found that it is 4π^2 K^2 + ρ^2 / α^4 . The logic...

Hi Jason, I tried your approaches but I find it a bit difficult to understand fully. Maybe I don't have enough skills and a more 'mechanical' or brute force approach may be easier for me to understand. Now I will try once again the approaches you mentioned if I can get answer with it. Thank...

Dear Jason, Thank you so much for the great help and giving priceless time to guide me in solution of this integral. I am trying to solve it with the approaches you mentioned. I hope I can find a reasonable solution to this integral. I also tried to solve the integral with using the formula...

Hi Jason, First, thank you so much for the reply. I am struggling with the doing the integrals. I tried and tried but couldn't get the result.

Hi thanks for the reply. The parameters ##\sigma_i## and ##\sigma_j## corresponds to the spread of spectral density and ##\delta_{ij}## is the width of the correlation between the i and j components of a field. and sign (i, j) = 1 when i = j and sign (i,j) = -1 if i is not equal to j.

Where , rho 1 and rho 2 are two dimensional position vectors and K is a two dimensional vector in the Fourier domain. I encountered the above Eq. (27) in an article and the author claimed that after integration the right hand side gives the following result: I tried to solve this integral but...