Recent content by rmjmu507

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 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 the initial guess is sufficient? Is there anything wrong with the exponential guess, or will both serve as solutions to the wave equations given?

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...

But then this isn't the difference between the transverse forces just to the left and right of the mass, it's the sum, no?

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...

I thought that because Ar is moving in the other direction, it's magnitude is opposite and therefore the - sign...is my logic incorrect? Here are the equations I have for the incident, reflected, and transmitted waves: yi=Aiei(ωt-kx) yr=Arei(ωt+kx) yt=Atei(ωt-kx) So, taking the...