Orbital angular momentum Definition and 83 Threads

Homework Statement Solve for ##L^2_x## ##L_x = \frac{\hbar}{i} (-sin(\phi)\frac{d}{d\theta} - cos(\phi)cot(\theta)\frac{d}{d\phi}##** the d's should be partial derivatives, but I'm not sure how to do that symbol. Sorry! Homework Equations Solve for ##L^2_x## ##L_x = \frac{\hbar}{i}...

Homework Statement i need to calculate the orbital angular momentum for 3D isotropic harmonic oscillator is the first excited state The Attempt at a Solution for the first excited state...

From "Modern Quantum Mechanics, revised edition" by J.J. Sakurai, page 196. Equation (3.6.4), 1-i \left( \frac{\delta \phi}{\hbar} \right) L_z = 1 - i \left( \frac{\delta \phi}{\hbar} \right) (x p_y - y p_x ) Making this act on an arbitrary position eigenket \mid x', y', z' \rangle...

Hi guys, I have a question which is probably stupid. I am studying angular momentum and I have found almost everywhere that, if we have orbital angular momentum higher than \ell=0 then it brings powers of the momentum of the system like k^\ell. What is the reason of that? Can someone suggest a...

This is a very basic question, but what is orbital angular momentum actually? I know it can be quantized as zero, 1, etc. What is it in layman's terms? I tend to understand it in terms like the Earth orbiting the sun. Spin on the other hand is either right or left spin. So what do the different...

Homework Statement What are the orbital angular momentum possible values for an electron in a hydrogen atom with a principal quantum number n = 3? Homework Equations L = \sqrt{l(l+1)}\hbar The Attempt at a Solution Possible values for l are 0, 1, 2. So, substituting these in...

Homework Statement We have a system of 2 indistinguishable spin-1 bosons. We shall adopt the center of mass frame. Let S = total spin L = relative orbital angular momentum J = L+S = total angular momentum Prove that J = 2m where m is an integer. If given that J=1, what are the permissible...

I am trying to self-learn quantum mechanics pertaining to Lanthanide ions. For a given set of J and MJ quantum numbers in a valence 4f^2 electronic configuration, J=0,2,4,6 and MJ=0,6,-6. The |J,MJ> basis functions are |0,0>, |2,0>, |4,0>, 1/2[|6,6>+|6,-6>]+sqrt(1/2)|6,0>, and...

I have some doubts about the implications of the orbital angular operators and its eigenvectors (maybe the reason is that I have a weak knowledge on QM). If we choose the measurement of the z axis and therefore the Lz operator, the are the following spherical harmonics for l=1...

We know from classical mechanics that angular momentum L = r \times p depends on your choice of origin. My question is: How does this work quantum mechanically? We know we get certain eigenvalues, but does this apply only in a certain choice of origin? How do we calculate angular momentum at...

Homework Statement Consider a spin-1/2 particle whose state is |\psi \rangle = \psi_+(\textbf r) |+\rangle + \psi_-(\textbf r) |- \rangle. Let \hat{ \textbf S } be the spin observable and \hat{ \textbf L } the orbital angular momentum. We assume that \psi_+(\textbf r) = R(r) \left(...

Homework Statement given a certain state |ψ> that is an eigenstate of L^2 and Lz Calculate <Lx^2> and <Lx> Homework Equations L^2|ψ> = l(l+1)h^2 Lz|ψ> = mh|ψ> Lx = YPz - ZPy The Attempt at a Solution <Lx^2> = (1/2)(h^2)[l(l+1)-(m1)^2] for Lx i got <Lx> = ∫ψ(YPz-ZPy)ψ dx

Can anyone describe an experiment that would be used to measure orbital angular momentum?

Satellite of mass m is moving with velocity v in a circular orbit of radius r about mass M. Find the orbital angular momentum. Know v = \sqrt{\frac{GM}{r}} Orbital angular momentum of a system is defined as the angular momentum of the center of mass of the system. Let the origin be at mass...

What is orbital angular momentum? Is it associated to the revolution of electron around nucleus?

Homework Statement Please see attached. I have two questions: how does pr get to be -ihbar (D/Dr + 1/r) ? where does the extra factor of D/Dr come from? one comes from r.del, but what about the other? surely div (r/r) = 2/r? Also, why does [r,pr]=-ih[r,D/Dr] = ih? surely...

Hi, I have read several texts where it says that the paramagnetic behavior of O2 molecule is due to two unpaired electrons in a degenerate pi* orbital. I have not read, however, any comment about the orbital angular momentum of these pi* states. Is there any reason why the orbital...

Homework Statement In part A I know that I must use L = mu*Sqrt[GMa(1-e^2)], but for the variable 'a' do I use the semi-major axis of Jupiter or the semi-major axis of the reduced mass? Homework Equations The Attempt at a Solution

Why is the s,p,d,.. nomenclature derived for the H atom also valid for many-electron atoms?

Homework Statement There is a binary system accreting via Rcohe lobe overflow, where mass is transferred fromthe donor to the accretor and then lost in an isotropic wind. State an expression for the orbital angular momentum of the accretor, J1 and then use keplers third law to find an...

I was asked for the energy and orbital angular momentum of a hydrogen atom in the 6f state. Thus, with n = 6 I found E to be -0.378, a straightforward calculation. I am confused about L, though. L = sqrt[l(l+1)]. Since n = 6, I thought l = n-1, so L would be sqrt(30)*h-bar, but the answer is...

Homework Statement Considering a two-body problem, star-planet, prove that the angular momentum of the planet is given by: \begin{equation} {\cal L}_{e} = {\mu}\sqrt{GMa(1-e^2)}, \end{equation} $\mu$ is the reduced mass M is the star mass a and e are the semi-major axis and...

When I was trying to learn the reason for the Orbital angular momentum quantum number taking only whole number values, I stumbled across the wiki site on the same, which says that, Angular momentum in quantum mechanics In quantum mechanics, angular momentum is quantized – that is, it...

From Carroll and Ostlie “An Introduction to Modern Astrophysics” prob 2.6 b After determining angular momentum of sun-jupiter orbit system in part a, the question then asks you “What contribution does the sun make toward the total orbital angular momentum. It says assume Jupiter is in a...

Homework Statement Consider a particle that moves in three dimensions with wave function \varphi . Use operator methods to show that if \varphi has total angular momentm quantum number l=0 , then \varphi satifies L\varphi=0 for all three components L_\alpha of the total angular momentum L...

Homework Statement In lectures and textbooks the lunar orbital angular momentum is given as: A = m/(1 + m/M)xR2x\omegaL But if the distance r of the moon from the centre of mass of the Earth-moon system is given by: mxr = Mx(R-r); so r = MR/(M +m) = R/(1 + m/M) and so the moon's angular...

How does the orbital angular momentum of two electrons in the same shell and same energy state cancel each others orbital angular momentum, provided both electrons have opposite spin?

The Uncertainty Principle is largely mathematical. For any two probability densities, if one is the Fourier Transform/Inverse Fourier Transform of the other, then the product of their variances is always greater than zero. Thus, energy and time, and momentum and position, via the squared...

Hello, sorry I am new to this forum, I hope I found the right category. I have a question about the momentum operator as in Sakurai's "modern quantum mechanics" on p. 196 If I let 1-\frac{i}{\hbar} d\phi L_{z} = 1-\frac{i}{\hbar} d\phi (xp_{y}-yp_{x}) act on an eigenket | x,y,z...

Why can't an electron in a coulomb field have an orbital angular momentum quantum number higher than it's principal quantum number (ie there is no 1p state etc.) I think is probably something I learned at one point, but I've forgotten and can't seem to find anything about it anywhere. I know...

Awesome forum here! I'm stuck on a homework problem and need some guidance. A H-atom exists in a 3px state. What would be the result of measuring the total orbital angular momentum of this state (e.g. 100 measurements)? I assume when they say 100 measurements that they mean the...

1. A proton of mass rotates with an angular speed of 2*10^6 rad/s in a circle of radius 0.8m in a cyclotron. What is the orbital angular momentum of the proton? 2.An object's angular momentum changes by 10Kgm/s^2. What magnitude average torque acted on this object? 3. A pulsar which emits...

Have you guys heard of this: http://www.sciam.com/article.cfm?chanID=sa006&colID=5&articleID=0001A73A-45BC-1F7F-82D883414B7F0000