I'm pretty confused by the rules regarding the total energy, the kinetic energy, and potential of a QM system.
Does the total energy have to be positive or greater than zero? And if so, why not? I don't really understand what it means to have a negative total energy of a system I guess. I...
Hey, I'm pretty confused by this relativistic collision problem.
A particle of mass m moving along the x-axis collides elastically with a 2nd particle of identical mass at rest in the lab frame and scatters. Its final momentum makes an angle theta with the x-axis in the lab. If its initial...
Okay- I guess I was being stupid and trying to make them also orthogonal to each other. I assumed that the Hamiltonian had to be Hermitian- but the matrix I obtained isn't symmetric, (by the way, why not, I thought the Hamiltonian counts as an observable and has to be Hermitian?)
So I got...
Thank you Diazona for your reply,
Firstly, sorry- I wrote the problem wrong, it should actually be
H = i\Delta(|w1><w2| - |w2><w1|)
in which case, is my matrix correct?
I still can't manage to get linearly independent eigenvectors... Also your explanation made quite a lot of sense to me...
Homework Statement
I am given the Hamiltonia operator of a system in two-dimensional Hilbert space:
H = i\Delta(|w1><w2| + |w2><w1|) and am asked to find the corresponding eigenstates.
I wrote this operator as a matrix, where H11 = 0, H22 = 0, and H12= i\Delta and H21= -i\Delta...
Not sure if this is in the right subforum but:
A chain of uniform mass density, length b, and mass M hangs in a loop from the ceiling (both its ends are adjacent to each other) At time t = 0, one end, end B is released. Find the tension in the chain at point A after end B has fallen a distance...
Homework Statement
Three beads of equal mass m are constrained to lie on a circular hoop of radius a = 1. The beads are connected by identical springs of spring constant k. The equations of motion for displacements are (I am going to use x, y, and z, where x = theta 1, y = theta 2, z =...
OOOh, I see, I used the singularities and I get pi/sqrt2 which I think is right. Thank you guys so much. I actually have another related question now though. First of all, why does sqrt(i) not work when I use it as z?
Also,
I'm now trying to do:
integral (0 to infinity) of sin(x^2)...
Homework Statement
the integral of 1/(1+x^4) from -infinity to +infinity
Homework Equations
Residue theorem.
The Attempt at a Solution
1/(1+z^4) so z^4 = -1
I know I should be using the residues at z = -sqrt(i) and z= i*sqrt(i)
I am getting a complex number as an...
Homework Statement
Given that \nabla2 1/r = -4\pi\delta3(r)
show that the solution to the Poisson equation \nabla2\Phi = -(\rho(r)/\epsilon)
can be written:
\Phi(r) = (1/4\pi\epsilon) \int d3r' (\rho(r') / |r - r'|)
Homework Equations
The Attempt at a Solution
I know...
ah nvm i realized its just optimizing a function with another contraining function.. i think... so i could use lagrange multipliers
thanks for your help
Homework Statement
Find the point on the curve defined by 5/8 x^2 - 3/4 xy + 5/8 y^2 = 1
That is closest to the point (1,-1)
Homework Equations
The Attempt at a Solution
I started by finding the gradient vector. < (5/4x - 3/4 y) , (5/4y - 3/4x) >
I could not figure...
Err, oh well whatever, I just did
flux = B x area of annular ring
change in flux = 2 times above
And about the point of the problem, perhaps it would help to know that there is a final part that i didn't post because I thought I understood how to do it if I did the above correctly: it asks:
...
I looked up "low Earth orbit" and that's supposed to be the locus of points from the surface up to about 6.5x10^6. For my area, I used the area between the larger circle and the smaller, surface one. I used a uniform magnetic field though. I just got back from spring break though and I can't...