Hi, I need help with some basic fourier transform properties stuff - its fairly simple though I think I am doing something wrong.
So we know from the shifting property
if h(x) has the fourier transform H(f)
then h(x-a) has the fourier transform H(f)ei*2*π*f*a
so I have the function
cos(2πf0x...
I think I see what you are saying. I will give a little more information into what I am trying to do.
The question is:
Consider two normalizable wave functions Ψ1(x, t) and Ψ2(x, t), both of which are solutions
of the time-dependent Schrodinger equation. Assume that the potential function is...
We aren't given any. Some other information which might be helpful though, the wave function is normalized, it is a solution to the time dependent schrodinger equation and the potential function is real. And again it approaches zero as x goes to +- infinity. Is that enough?
Homework Statement
If I have a wave function that goes to infinity can I assume that the derivative also goes to 0 at infinity?
Homework Equations
The Attempt at a Solution
The reason I think it does is because the wavefunction and its derivative must be continuous everywhere...
Homework Statement
Hi, I hope this isn't a silly question. I am looking to find the mean potential energy of a mass on a spring with spring constant k and maximum displacement x0.
Homework Equations
The Attempt at a Solution
I know the maximum energy is 1/2*kx0^2 so would the...
I did some work on c, hopefully someone can give me a reply to this to make sure I am on the right path.
so I said that the solution is similar to the finite potential well. In region A which is between -b and -a the wavefunction is of the form:
\psi = Aexp(kx) + Bexp(-kx) (I know that...
Homework Statement
The question is attached as a picture. Note: if someone would prefer I type it out I can.
Homework Equations
Schrodingers equation
The Attempt at a Solution
PART A
I am pretty sure I got the well right. It looks like a finite well inside an infinite well. I...
Homework Statement
Hi I actually have three questions that I am posting here, help in all of them would be greatly appreciated!
1) Prove that ln(n!) ≈ nln(n)-n+ln(2*pi*n)/2 for large n
2)Supposed you flip 1000 coins, what is the probability of getting exactly 500 heads
3) Show that n! =...
Homework Statement
We have to estimate the ground state energy of an infinite potential well (1d) using an argument based on the heisenberg uncertainty principal. We then are supposed to compare it with the exact value from the eigenvalue equation.
Homework Equations
Below
The...
Homework Statement
Starting from the Planck-Body Law
I_{λ}dλ = \frac{2\pi c^{2}h}{λ^{5}} \frac{1}{e^{hc/(λkT)} - 1}dλ
where λ is the wavelength, c is the speed of light in a vaccuum, T is the temperature, k is Boltzmann’s constant,
and h is Planck’s constant, prove that the total energy...
I mostly understand that. The answer the book gives for I free is = (I*pi*s^2)/(pi*R^2) which makes sense, but I am looking for what definition they used exactly to get that. What equation?
Homework Statement
I am looking at an example problem in the text and they skipped some steps. I think I am missing somthing obvious but none-the-less I don't know what is going on.
We have a long copper rod o radius R which carries a uniformly distributed (free) current I. Find H, the...
Homework Statement
One end of a long horizontal string is attached to a wall, and the other end is passed over a pulley and attached to a mass M. The total mass of the string is M/100. A Gaussian wave pulse takes 0.12 s to travel from one end of the string to the other.
Write down the...
Hi guys, so I figured out my main problem with this question. I am having troubles coming to terms with the fact that were using a cylinder but the charge is given in terms of the linear charge density. So when using gauss's law, what is the charge enclosed? Is it just lamba * l?
sorry I wiorked a little bit, is the electric field E = λ/(2*ε0) * (s^2-a^2) where s is the radius on between a and b?
Edit:
I did some looking around and worked a little more and here is where I am at. The electric field in between the two cylinders is \frac{λ}{2*pi*ε0 * s} where s is...
Homework Statement
There are 2 long coaxial insulating cylinder. The inner and outer cylinders have radii of a and b and charge densities λ and -λ uniformly distributed on the surface. Calulcate energy per unit length 2 ways (equations below)
Homework Equations
W = \frac{1}{2}\int σ...
Homework Statement
Two-dimensional SHM: A particle undergoes simple harmonic motion in both the x and y directions
simultaneously. Its x and y coordinates are given by
x = asin(ωt)
y = bcos(ωt)
Show that the quantity x\dot{y}-y\dot{x} is also constant along the ellipse, where here the...
So
=\frac{[V_{y}(x,y,z)-V_{y}(x, y-\frac{1}{2}Δy,z)]}{\frac{1}{2}Δy}
=V_{y}(x,y,z) - V_{y}(x,y,z) + \frac{∂v_{y}}{∂y}(\frac{1}{2}Δy) / (\frac{1}{2}Δy)
=\frac{∂v_{y}}{∂y}
correct?
Sorry for the poor formatting I am still getting used to this latex stuff
Homework Statement
In deriving the formula
div v = \frac{∂v_{x}}{∂x} + \frac{∂v_{y}}{∂y} + \frac{∂v_{z}}{∂z}
we used a rectangular solid infinitesimal volume; however, any shape will do (although the calculation gets harder). To see an example, derive the same formula using the prism-shaped...
hm. I can see how that works now but do you think you can explain that a little further if possible?
Also that means then I have this left with the appropriate substituitons:
\frac{1}{2}[3B_{0i} - B_{0l}δ_{li}]
so then δ_{li}] = 1 only if l = i or 0 if l ≠ i
changing indicies...
well it would equal 1 only if the indices are equal so then is it equal to 3 also? (because of the y and z components)?
edit: looking only at the x component the indicies are summed to 3 so for the x component is it equal to 3?