Recent content by gysush

Consider the Helmholtz Equations with a perturbation p(r) [gradient^2 + p(r) + omega^2/c(r)^2 ]u(r,w) = 0 Does anyone know where I can find resources to the solutions/discussion of this equation? I can find many things such that p(r) = 0 , but the RHS = forcing function, but that is not...

laplace transform The solution involves Laplace transforms. Closed.

A question about an integral encountered in a paper I am reading about Green's Functions of the acoustic wave equation ... The integral encountered: Im{Integrate[ exp((i*y-a)*k), dk, 0, Infinity]} = Re{1/(y+ i*a)} where i = sqrt(-1) and a,y,k elements of R. Been a while since I've calculated...

Consider a matrix A(i,j) What I want to do example: A= [1 2 3; 4 5 6; 7 8 9] I want to to display 1 2 3 4 5 6 7 8 9 I will then save it to a file; I know how to do that. But how do I get MATLAB to display the individual elements sequentially? Thank you. *edit* Nevermind figured it out...

Consider a two level system of N distinguishable particles. We want to find the Energy of the system as a function of the Temperature. The first energy level is E1 and the second is E2. I computed the entropy. Now if we take a derivative with respect to Energy, we have 1/T = dS/dE where...

Given that E(n) = (n^2)E, and that our wave function PSI = 1/Sqrt(14)(Psi(1) + 2*Psi(2) + 3*Psi(3), what is the the value for the measurement of the energy? So, <H> = SUM((c(n)^2)*E(n)) where E(n) = (n^2)*E and c(1)=1/sqrt(14), c(2)=2/sqrt(14), c(3)=3/sqrt(14), which satisfies...

Yes, thank you as well. But the answer fell out almost trivially (since I already know Integral[sinx/x] once I did the integration by parts. Just had to make sure I took out the b or the a once I diff cos(ax)

Thank you!

I'm working on a complex analysis problem from Arfken. Integrate[ (cos(b*x)-cos(a*x))/(x^2), {x, -Infinity, Infinity}] and show that it is equal to Pi*(a-b) Attempt: I first look at a related problem (or one that I think is related). => f(x) = sin(x)/x => f(z) = sin(z)/z...

Sorry, hope I didn't mean to sound like I was yelling or questioning your help in my response. Thank you for your response about the plane! I can see what is happening better now.

How does my solution not satisfy? http://www.wolframalpha.com/input/?i=1/3*1/3*{{1,2,2},{2,1,-2},{2,-2,1}}.{{1,2,2},{2,1,-2},{2,-2,1}}

I guessed the solution by just trying to make the the squares of the components of the columns equal to 1. Then multiplied the transpose and made terms negative such that they equal 0 when appropriate. So I got that A = 1/3*{{1,2,2},{2,1,-2},{2,-2,1}} This satisfies A*A' = I. However, what would...

Find an orthogonal matrix whose first row is (1/3,2/3,2/3) I know orthogonal matrix A satisfies A*A' = I, where A' is the transpose of A and I is identity matrix. Let A = 1/3*{{1,2,3},{a,b,c},{d,e,f}} where a,b,c,d,e,f elements of R A'= 1/3*{{1,a,d},{2,b,e},{2,c,f}} We can obtain...

Ahh...I forgot to remember that a norm for F=C requires we take the complex conjugate of the 2nd vector. You beat me to to it. :-)

We want to find a basis for W and W_perpendicular for W=span({(i,0,1)}) =Span({w1}) in C^3 a vector x =(a,b,c) in W_perp satisfies <w1,x> = 0 => ai + c = 0 => c=-ai Thus a vector x in W_perp is x = (a,b,-ai) So an orthonormal basis in W would be simply w1/norm(w1) ...but the norm(w1)=0 (i^2 +...