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...
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...
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...
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...
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...
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...
Homework Statement
We will see (in Chap. 5) that the magnetic field can be derived from a vector potential function as
follows:
B = ∇×A
Show that, in the special case of a uniform magnetic field B_{0} , one possible
vector potential function is A = \frac{1}{2}B_{0}×r
MUST USE TENSOR NOTATIONm...
Homework Statement
This is a coursework problem. I am having issues understanding the concepts on this one topic - divergence and how it relates to flux. I have attached screenshots that honestly give the best representation of my issue but I will set up the issue I am having...
Homework Statement
This is more of a imaging/physiological course but it uses convolutions and i can understand the applications, i just need help writing the matlab script to give meaningful answers.
The problem asks that we use matlab to convolute 2 functions:
x(t) = a*tb*exp(-ct)...
1.A rigid structure consisting of a circular hoop (on the right) of Radius R and mass m, and a square (on the left) made of four thin bars, each of length R and mass m. The rigid structure rotates at a constant speed about a verticle axis, with a period of rotation of 2.5 s. Assuming R = 0.50m...