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...
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...
Homework Statement
Consider the Earth’s magnetic field as that of a dipole with the magnetic field around the equator having magnitude 30 µT. The radius of the Earth is 6.37 106 m.
a. Calculate the magnetic flux φB in low Earth orbit (r=6.5x10^6 m) at the equator, in units of Tm2.
b...