Recent content by ourio

Homework Statement A particle of mass m is subject to the one dimensional force F = x-x^3. Determine whether or not this force is conservative. If it is: a) write the scalar potential and find the turning points, b) write the kinetic energy and show that the sum of the kinetic and potential...

OK... I think I may have got some of it... The 2p state of hydrogen has \ell=1 with m\ell=-1,0,1 So the 2p state splits into three levels by the external B. Calculating the gLande factor for the 2p state as \frac{4}{3} and the 1s state as 2, I find that the splitting of the 2p state is...

Homework Statement A Hydrogen atom is subjected to a magnetic field strong enough to overwhelm the spin-orbit coupling. Into how many levels would the 2p level split? What would the spacing be in the terms of Bext, e, me, and \hbar Homework Equations I know that I have to use the gLande...

Thanks. I think I've got it now... it just took some time staring at the problem! Thanks again.

Okay, so if it really is the derivative of the magnitude, I can understand that. But, what does \ (\vec{r(t)} \bullet \vec{r'(t)})^{1/2} equal? If you replace r with something like f(x)+g(x) and r' with f'(x)+g'(x) and do the dot product, you get \sqrt{f(x)f'(x)+g(x)g'(x)}. But how would...

Homework Statement Prove that, if \vec{r}(t) is a differentiable vector valued function, then so is ||\vec{r}(t)||, and \vec{r}(t) \bullet \vec{r'}(t) = ||\vec{r}(t)|| ||\vec{r}(t)||'Homework Equations I know how to do a dot product, but what bothers me is the fact that the question involves...

Oh, I'm an idiot! Of course the complex number isn't in the sine! Thanks Doc Al for all of your help! I'll never forget about Euler's formula again! :)

OK... so I found that the original equation can be written as follows: Aeikxe-iwt Using Euler's formula on the eikx gives: Ae-iwt (cos(ikx)+i sin(ikx)) I know that the cosine term will eventually cancel when I subtract. But the complex number in the sine bothers me. Won't that end up being a...

Thanks for the hint about Euler's formula... it really helped. So from the original equation, I now have: A[cos(kx-wt)+i sin(kx-wt)]-A[cos(-kx-wt)+i sin(-kx-wt)] I distributed the A term throughout, and found that the cosine terms canceled. I was left with: Aisin(kx-wt)-Aisin(-kx-wt)...

That's the thing... I'm not sure. If I had to guess, I would say it would look something like: Aei(kx-\omegat) - Bei(-kx-\omegat) But how do I relate it to sine?

Homework Statement A wave in quantum mechanics is represented by Aei(kx-\omegat). Show that a standing wave looks like 2iAe-i\omegatsin(kx) by subtracting two waves moving in opposite directions. (Hint: make the k negative in one of the waves) Homework Equations As far as I know, the 2...