Homework Statement
A particle in a box of width 2a is in a state \psi=\frac{1}{\sqrt{2a}} for |x| less than or equal to a and 0 for |x| greater than a. What is the probability of finding the particle in [-b, b] inside the box? What is the probability of finding the particle with momentum p...
Homework Statement
Sketch d-orbital splitting diagrams for a complex in Td symmetry and a complex in D4h symmetry. Label the orbitals as bonding, antibonding, or non-bonding
Homework EquationsThe Attempt at a Solution
So I know that in Td symmetry, the d-orbitals split into a lower...
Homework Statement
I'm trying to construct a molecular orbital correlation diagram for a tetrahedral compound [NiX4]2- considering the ligand pi-orbital basis. I've already constructed a diagram wherein the only the sigma-orbital basis is considered. In that diagram, I had 12 electrons for the...
I see...I was considering this equation as only a two-dimensional one...for some reason I was overlooking the x component in the cosine function. Not entirely sure why, perhaps because of the E(y,z) term, but I now realize this is simply a coefficient corresponding to the amplitude.
Thanks!
I was able to get the k_x^2 term by determining \nabla^2\textbf{E} and rearranging, thus obtaining the desired relation.
However, I'm not entirely sure why it's necessary to determine \nabla^2. Can someone please explain this to be?
Homework Statement
Show that the solution \textbf{E}=E(y,z)\textbf{n}\cos(\omega t-k_xx) substituted into the wave equation yields
\frac{\partial^2 E(y,z)}{\partial y^2}+\frac{\partial^2 E(y,z)}{\partial z^2}=-k^2E(y,z)
where k^2=\frac{\omega^2}{c^2}-k_x^2
Homework Equations
See above.
The...
Homework Statement
Show that if the displacement of the waves on a membrane of width b is given by the superposition
z=A_1\exp^{i(\omega t-(k_1x+k_2y))}+A_2\exp^{i(\omega t-(k_1x-k_2y))}
with z=0 when y=0 and y=b then the real part of z is
z=2A_1sin(k_2)sin(\omega t-k_1x) where...
Homework Statement
I've determined the dispersion relation for a particular traveling wave and have found that it contains both a real and an imaginary part. So, I let k=\alpha+i\beta and solved for \alpha and \beta
I found that there are \pm signs in the solutions for both \alpha and \beta...
So a more all-inclusive/comprehensive/safer guess would be something like:
E=A*exp^{i(wt-kz)}
Thus, if the initial conditions are E(0,0)=0 the sine function is returned and if E(0,0)\neq0 then the cosine function is returned?
Please let me know if this is a better guess to make when dealing...
Homework Statement
There is no specific problem - this is more of a broad question...given a wave equation and asked to write down/guess an expression/general solution for a traveling wave, it is sufficient to say the following:
1) For \frac{\partial^2 E}{\partial z^2} -...
Homework Statement
How can I draw a Lewis dot structure for octathiocane (S8) which is non-cyclic, net neutral, and which does not violate the octet rule?
Homework Equations
None.
The Attempt at a Solution
First, I tried drawing a straight chain molecule, but the two terminal...
I tried flipping the signs, but I'm still not able to derive the given ratios...
Here's what I have:
T*k*i*eiωt(Ai-Ar+At)=M*i2*ω2(Ai-Ar+At)*eiωt
Cancelling terms,
T*k*(Ai-Ar+At)=M*i*ω2(Ai-Ar+At)
I made the following substitutions: k=ω/v, Z=T/v, Z=ρc, and the substitutions...
I realize that the slope across the interface (the mass) must be the same...
Normally, I would say that:
T∂yi/∂x + T∂yr/∂x = T∂yt/∂x across an arbitrary point on the string.
However, the problem states that the difference between the transverse forces just to the left and right of the...