OK. So we have a soap bubble, with P_0 outside the bubble \gamma for a surface tension on the bubble. So the Pressure inside denoted
P_A:=\frac{4\gamma}{R}+P_0.
Now if that bubble expands say to a radius, S for whatever reason, does P_A remain constant inside, to give me a set of...
What does it mean for a bubble to be in equilibrium?
I assumed it just meant that the forces expanding it and the forces compressing it were equal, hence it was at a steady radius. Is there more to it than that?
I'm working on an EM problem so I don't think the specifics are important, I...
I've searched google for some decent tables but couldn't find any. I'm trying to collect
Normalized Spherical Harmonics
Associated Legendre Polynomials
Zeros of the Spherical Bessel Function
Normalized Radius Function for the Hydrogen atom
etc.
I'm allowed a sheet with as much of these...
Yah, I ended up using inner products and it all worked out. It's not that the problem was hard, the method just didn't seem of appropriate length. My professor is inconsistent with homework trends.
That was my first instinct, which gave me l=1, m=0. But the e^{(-r/a)} made me think that n=1, which then threw out my l (since l<n). Also the r^2, made me think n=2, but in either case I didn't see any good linear combination jumping out at me.(and it definitely wasn't just 210) I'll look at...
A hydrogen atom is in the state \psi=Ar^2e^{-r/a}cos(\theta).
I need to find lowest energy state and etc. Obviously normalize to find A, but I'm not seeing the obvious linear combination of wave functions; and I really don't think my instructor wants me to do several inner products (plus...
Yes, but \langle v_0|[H,A]|v_0 \rangle =0 which gives me a trivial inequality, which leads me to believe something is incorrect and hence why I posted here.
Let H=\hbar\omega \[ \left( \begin{array}{ccc}
1 & i & 0 \\
-i & 1 & 0 \\
0 & 0 & 1 \end{array} \right) \]
and let A =\hbar \left[ \begin{array}{ccc}
1 & 0 & i \\
0 & 1 & 0 \\
-i & 0 & 1 \end{array} \right].
Calculate the uncertainty relation \sigma_E \sigma_a for a system in the energy ground...
So I achieve eigenvalues of \{0,1,2\} (this is actually the eigenvalues I have for the problem), would the 0 or the 1 be the lowest state? I assumed 0, but can a ground state have 0 energy?
When given a Hamiltonian operator (in this case a 3x3 matrix), how do you go about find the ground state, when this operator is all that is given? By the SE when have H\Psi=E\Psi. I can easily solve for Eigenvalues/vectors, but which correspond to the ground state, or am I missing something?
If you're asking where the operation comes from, I believe it's because it was needed to make \mathbb{M}^{m\; \x\; n} the vector space, and to easily represent the linear transformation's operations. There are other ways to define it, though I believe we use this one for convention.
An...
Actually I believe that "Baby Rudin" is known as the most user-friendly text in basic analysis. It is the standard text for a reason. I can't think of anything better but the standard text for Reals would be Real Analysis by Royden. It covers many of the same things, so perhaps another nice...
I first learned of it in a PDE course dealing with Sobolev spaces. Real Analysis by Folland and PDE by Evans both have a decent introduction in the latter part of the books. Folland gives the information to understand it in the previous part (though I found Folland to be quite difficult unless...
Well I was dealing with a subset where it did make sense.
Let me just ask a different question:
If \{h_n\} is a sequence in H and \Sigma^\infty_{n=1}||h_n||<\infty and I show that \Sigma^\infty_{n=1}h_n converges in H; does that imply that H is complete?