Recent content by Thadis

Hello, I am having to find the rotational diffusion of a magnetic particle inside of water. I already have a diffusion coefficient but I do not know how to take into account the restoring force that the particle will feel from the magnetic field. The info that I know is: B-Field Strength...

Ahh d\sigma=r^2sin(\theta) d\theta d\phi. Forgot that it was not just dd/theta d\phi So that means that it would be \iint r^6/5*sin(\theta)*d\theta*d\phi if the limits are \theta=0 to pi and \phi=0 to 2pi?

Sorry, was typing that in a hurry saying I was having to leave right then. What I was trying to say, since the normal to the sphere is the normalized position vector, which would be {x,y,z}/5 since we know the distance to the surface is 5. If we dot this into the force that would create...

I was just thinking about it but would actually turning it into a surface integral make it easier? Saying you would have the double integral of the force dotted into the normal, which would give out (x^2+y^2+z^2)^2/5 since the normal to the sphere is just the normalized position vector? And...

Ahh, I knew I was forgetting something. For this case once I converted x,y, and z into sphrerical coordinates wouldn't the limits of integration be r=0 to r=5, θ= 0 to 2pi, and \phi=0 to 2pi? Also just to double check. Would taking the volume integral actually easier in this case?

Homework Statement Evaluate the integral as either a volume integral of a surface integral, whichever is easier. \iiint \nabla .F\,d\tau over the region x^2+y^2+z^2 \leq 25, where F=(x^2+y^2+z^2)(x*i+y*j+z*k) Homework Equations \iiint \nabla .F\,d\tau =\iint F.n\,d\sigma The...

It is suppose to be a Hermitian matrix. They both should be -1, sorry about that. And I believe I have an approximate answer. I believed I just changed the way I did it and use the face that for a unility matrix that U-dagger =U-1 and it was much cleaner output. Thanks for your help!

Homework Statement Compute the inverse, eigenvalues and eigenvectors of the following matrix, M. Are the eigenvectors orthogonal? Determine a unitary similarity transformation matrix U such that U-1MU is diagonal.With M being {2, 0, 2i, 0, 1} {0, -1, 0,-2i,0} {-2i, 0, 1, 1, 1} {...

Homework Statement Write sin(7t)-sin(6t) as a product of two trig. functions. Homework Equations e^(ix)=cos(x)+isin(x) sin(2x)=2cos(x)sin(x) cos(2x)=cos^2(x)-sin^2(x) The Attempt at a Solution I do not really know how to approach this. I have tried using the sin(2x) identity...

I think I actually have solved it. I was right with the PV=nkT, I believe I previously messed up with the algebra. Homework Statement Using the same meathod as in the text, calculate the entropy of mixing for a system of two monatomic ideal gases, A and B, whose relative proportion is...

Yeah I have done it and it also was explain in the physics textbook. After thinking about it and just hearing a couple of additional things from other places online I think I am making more sense of everything. Thanks again for all of the help!

Oh wait I think I understand what now what it is. Basically for the second one what was my problem was I wasn't thinking about taking the conjugate of the two matrices multiplied together and multiplying it by the original matrix. The reason why I am confused is just that we have just spent...

I think looking over a couple more questions I have I think mostly where I am getting confused is what to do with the |<u|w>|^2 operator even in the first place. I apogolize for not knowing more about this subject its just I have nowhere really to explain the details of a problem of this sort in...

Would it be that you can set the individual components of the sum to a value of |z|^2 since the indivudual components would follow the form of (u_i*)w_i?

Homework Statement Prove the following statements about the inner product of two complex vectors with the same arbitrary numbers of components. (a)<u|w>=<w|u>* (b)|<u|w>|^2=|<w|u>|^2Homework Equations 1. <u|w>=(u*)w 2. (c_1+c_2)*=c_1*+c_2* 3. c**=c 4. ((c_1)(c_2))*=(c_1*)c_2*The Attempt at a...