Homework Statement
Consider the motion of particle moving on the inside surface of a smooth cone of half-angle α, subject to the gravitational force. Although this problem does not involve a central force, certain aspects of the motion are the same as for a central-force motion.
Show that the...
Homework Statement
I am taking the surface integral over a quarter cylinder. Everything is fine and I can get the correct answer, it's just a conceptual problem that I need help with.
Homework Equations
The da for the "curved" outer surface is da=sd\phi dz\hat{s}
The da for the bottom...
Homework Statement
I am taking the surface integral over a quarter cylinder. Everything is fine and I can get the correct answer, it's just a conceptual problem that I need help with.
Homework Equations
The da for the "curved" outer surface is da=sd\phi dz\hat{s}
The da for the bottom...
Homework Statement
I want to plot the following function into Maple14. \vec{v}=frac{1}{\vec{r^{2}}} \hat{r}
**In case the latex is screwed this says v=r^(-2) *r-hat
The Attempt at a Solution
My code for Maple is the following, but it doesn't seem to work.restart; with(LinearAlgebra)...
If \psi(x+\langle x \rangle) is distributable (meaning f(x+y)=f(x)+f(y)) then I come up with the following:
\int{ x \psi^{*}(x+\langle x \rangle) \psi(x+\langle x \rangle)\,dx}
\int{ x[ (\psi^{*}x+\psi^{*}\langle x \rangle)( \psi x+\psi\langle x \rangle)\,dx}
\int{ (\psi^{*}\psi...
I've set it up the way you suggested, and the exponential terms computing \langle x \rangle cancel. However there is a \langle x \rangle term in \psi(x+\langle x \rangle). Is this not a discrepancy to have the value you are trying to calculate inside the equation for calculating its value...
Homework Statement
If <x> and <p> are the expectation values of x and p formed with the wave-function of a one-dimensional system, show that the expectation value of x and p formed with the wave-function vanishes. The wavefunction is:
\phi(x)=exp(-\frac{i}{h}\langle p\rangle x)\psi(x+\langle...
I'm not sure why PhysicsForums.com isn't displaying my latex properly so I have attached a PDF of the question.
Homework Statement
Show that, for a 3D wavepacket,
\frac{d\langle x^2 \rangle}{dt} $=$ \frac{1}{m}(\langle xp_{x} \rangle+\langle p_{x}x \rangle)
The Attempt at a...
I'm a TA and there is an inconsistency in what the solutions manual states and what the students are turning in, but both seem correct.
The Latex code isn't working properly for the post, but it is easy to see what equations are used
Homework Statement
A particle of mass m moves along the x...
Homework Statement
Problem 9.2(B) from Kittel Solid State Physics.
A two-dimensional metal has one atom of valence one in a simple rectangular primitive cell of a1 = 2Å and a2 = 4Å. Calculate the radius of the free electron Fermi sphere and draw this sphere to scale on the drawing of the...