Thank you for your help! You're right, I often make mistakes when quickly jotting down an integral without thinking, and the normalization tecnique will help me alot.
I would write E\int(Ylm)2cos\theta but i know there is more to it than that, a coefficient or something I am missing. Also I'm not sure about the bounds.----wait, just realized that I am looking for polar or spherical coordinates!
I am struggling with the same problem, I know the spherical harmonics Ylm are involved and I think we can use \Delta E = < l,m|Ecos \theta |l,m> because Ecos\theta is the hamiltonian here but I'm not sure how to put it together.
If you've figured it out please let me know!
-Felicity
Thank you for replying to my question,
About the i's
I realize now that I was assuming that λ was negative which is the condition for bound states but I realize that this was not a good assumption (turns out this only a well when λ <0) and that the i's should in fact be there.
About...
Homework Statement
consider the scattering matrix for the potential
2m/hbar2 V(x) = λ/a δ(x-b)
show that it has the form
(2ika/(2ika-λ) , (e-2kib) λ/(2ika-λ)
(e2kib) λ/(2ika-λ) , 2ika/(2ika-λ)
(I've used commas just to separate terms in the matrix)
prove...
Homework Statement
consider a potential given by
V(x) = infinity x < 0
= 0 x > a
= a negative function of x in between
suppose it is known that the interior wave function is such that
(1/u) (du/dx) at x=a = f(E)
a. what is the binding energy of a...
Thank you so much for the reply! I see my mistake now but I still have not solved the problem
I see now that
divA = 1/√g ∂i (√g Ai) = ∂Ai/∂xi + (1/√g ∂i √g )Al
which brings me to the hint
Гlil = 1/√g ∂i√g
which must be equal to
Гkij = gkl/2 (∂gil/∂xj+∂glj/∂xi-∂gij/∂xl)...
Homework Statement
show that the definition of the invariant divergence
divA = 1/√g ∂i (√g Ai)
is equivalent to the other invariant definition
divA = Ai;i
Ai;k = ∂Ai/∂xk + ГiklAl
Гkij = gkl/2 (∂gil/∂xj+∂glj/∂xi-∂gij/∂xl)
Homework Equations
g is the metric tensor...
Homework Statement
a particle is in the ground state of a box with sides x = + or - a. Very suddenly the sides of the box are moved to x = + or - b (b>a). What is the probability the particle will be found in the ground state for the new potential? What is the probability that the particle...
ok i separated variables, integrated and got
ψ(x)=e1/(2λ) x2
however I don't see how this can be square integrable since for any value of λ I can think of the integral of the square will equal infinity. I feel like I am missing something obvious here but I don't know what it is
Homework Statement
solve the eigenvalue problem
∫(-∞)x dx' (ψ(x' ) x' )=λψ(x)
what values of the eigenvalue λ lead to square-integrable eigenfunctions?
The Attempt at a Solution
∫(-∞)xdx' (ψ(x' ) x' )=λψ(x)
differentiate both sides to get
ψ(x)x=λ d/dx ψ(x)
ψ(x)x/λ=...
Thank you so much for your help, I see now how V(x) must be real as a potential energy function (except in cases of particle absorbtion and decay which I now know is what this problem is about). Again thank you for taking the time to help me with this problem.
Homework Statement
a 3D solid is bounded by 2 paraboloids. The binding condition in cartesian coordinates is
-1+(x2+y2) < 2z < 1-(x2+y2)
a) rewrite the binding condition in parabolic coordinates
b) using parabolic coordinates and the (already derived) metric tensor, find the volume of...