Recent content by laser1

ah ya it's 0 if it's outside isn't it so the 2nd derivative isn't continuous :(. Cheers

When I do this I keep getting a negative answer. Why? My workings: ##<O> = \int \psi* O \psi dx## in general. And ##\hat{p}=\frac{\hbar}{i} \frac{d}{dx}## so ##\hat{p^2} = -\hbar^2 \frac{d^2}{dx^2}##... And by plugging in ##\Psi##, I get ##<p^2>=-\frac{10\hbar^2}{3L^2}##. Any thoughts on why...

Thanks, I guess the justification is "a unit sphere by definition" then!

why unit sphere rather than an arbitrary sphere?

Where does the ##\sin \theta d\theta d\phi## come from? I had thought it came from the fact that the jacobian in spherical coordinates is ##r^2 \sin \theta## but maybe I was wrong.

In the solutions, I must integrate ##Y_1^0 Y_1^{\pm 1}##. But my concern is when it states that the differential element (I think area?) is ##d\theta d\phi##. I know that as then ##dA=r^2 \sin \theta d\theta d\phi##. But the solution only states ##\sin \theta d\theta d\phi##. Why is this? Also...

my lecturer uses the notation ##dF/dy## in the second last term. I am confused why it is not ##\partial F/\partial y## instead.

sorry, edited!

The above image is from my lecturer's notes. My concern is when it seems like my lecturer has split up the dF/dx term into dF/dy y' + dF/dy' y''. Why is it this as opposed to ##\frac{\partial F}{\partial y}## etc.? Or would this not matter, because y is an independent variable, and hence, the...

psi is given above. I have checked multiple times but can't find my mistake. Thank you!

Maybe instead of using the fact that integral of rho over all space is -e, I integrate it explicitly? I get the same answer, though.

How far away the proton and electron are from each other. 0 because equal charge. Good point. I tried this out though and got the integral of r delta(r) will turns out to be 0. Regarding the "hint" about the integral, I still don't see it! $$\mathbf{p}...

For this question, I get that $$\mathbf{p} = \int \mathbf{r}\,\rho(\mathbf{r})\,d^3r$$ but for the bounds, does r go from 0 to ##r_0## or from 0 to ##\infty##? I would think infinity, but then how do I use the "hint"? I also don't get the significance of shifting the electron charge density...

sorry if I am behind in logic, but I would like to clarify something. Are the fourier coefficients equivalent to the trigonometric coefficients? I believe they are. However, if they are, then I don't understand the logic.

What I think: All polynomials are taylor polynomials. What I also think: All taylor polynomials are polynomials. All german shepherds are dogs. All dogs are not german shepherds. So I don't think this analogy holds unless one of my statements above is incorrect.