Recent content by zhaos

I guess i have $$ |A|^2 \int_0^\infty dr r^2 \psi^*_{0,k'}(r)\psi_{0,k}(r) = \delta(k-k') $$ and ## \psi_0(r) = \sin(kr)/r = \frac{i}{r}( \exp(ikr) - \exp(-ikr))##, and the r^2 will cancel, and then one does the integral...

Homework Statement I think, to normalize a wavefunction, we integrate over the solid angle ##r^2 dr d\theta d\phi##. Typically we have ## R(r)Y(\theta, \phi) ## as solutions. If ##Y## is properly normalized, then the normalization condition for ##R(r)## ought to be $$ \int_0^\infty dr r^2...

Homework Statement Maybe I missed it, but in my notes and also in documents like (http://ocw.mit.edu/courses/physics/8-05-quantum-physics-ii-fall-2013/lecture-notes/MIT8_05F13_Chap_09.pdf) (equation 1.64), I see $$ \vec{r}\cdot\vec{p} = -i\hbar r \frac{\partial}{\partial r} $$ Where ##r## is...

Oh. That makes it clear. Thank you.

Homework Statement I was reading this textbook: https://books.google.com/books?id=sHJRFHz1rYsC&lpg=PA317&ots=RpEYQhecTX&dq=orbit%20center%20operators&pg=PA310#v=onepage&q=orbit%20center%20operators&f=false Homework Equations In the equation of the page (unlabeled), we have $$...

The identity operator can be written as $$ 1 = |1\rangle \langle 1| + |2\rangle \langle 2| \\ $$ For example suppose ##|\psi\rangle = c_1 |1\rangle + c_2|2\rangle## $$ |\psi \rangle = 1|\psi \rangle = |1\rangle \langle 1|\psi\rangle + |2\rangle \langle 2| \psi \rangle \\ = |1\rangle c1 +...

Hi there, thanks for you reply. I was able to understand your derivation after some studying of it. It does seem that my book offered no indication of this sort of derivation though, which disappoints me. Note. I wrote above that the Euler-Lagrange in generalized coordinates is...

Ok, so it goes on though. This text develops the Hamiltonian in generalized coordinates: H(q_1, ... , q_{3N}, p_1, ..., p_{3N}) = \frac{1}{2} \sum_{\alpha=1}^{3N} \sum_{\beta=1}^{3N}p_\alpha G^{-1}_{\alpha\beta}(q_1,...,q_{3N}) p_\beta + U(\mathbf r_1(q1,...,q_{3N}),...,.\mathbf...

That was tricky to see because of the way the terms were grouped. I worked it through, and now I get it. Thank you.

Homework Statement I need some help understanding a derivation in a textbook. It involves the Lagrangian in generalized coordinates. Homework Equations The text states that generalized coordinates {q_1, ..., q_3N} are related to original Cartesian coordinates q_\alpha = f_\alpha(\mathbf r_1...

a small bump? This was a conceptual question I had, not relating to any actual HW problem, so perhaps I shouldn't have asked it in this section. But basically it's either omega = (kappa/ I)^(1/2) or it's omega' = omega*thetamax*cos(omega*t), where omega in the second equation is defined by...

I'm not sure. Are all the data given compatible? Given all the data available to you, both methods seem to be ok.

Homework Statement Hi all, I am a bit confused about angular frequency, specifically in the case of a pendulum (bob pendulum or physical pendulum). Also, what's the difference between angular frequency and angular velocity? Homework Equations I understand that a physical pendulum is...

Hi PhantomJay Thanks for your reply. Since the block is slipping we would use mu k. I think the situation is now.. F - muk * m1 g = m2 * a [for block 2] and muk * m1 g = m1 * a' [for block 1] (a' not the same as a) Ah so I see what you mean about a' being independent of F. Thanks.

Hi all, I am studying for an exam and changed a practice problem by putting the force on the bottom block (you'll see). I just wanted to check if my thinking is correct. Homework Statement Two blocks sit on top of each other, block 1 (m1) on top of block 2 (m2), on a frictionless surface...