What is Orbital angular momentum: Definition and 83 Discussions

The orbital angular momentum of light (OAM) is the component of angular momentum of a light beam that is dependent on the field spatial distribution, and not on the polarization. It can be further split into an internal and an external OAM. The internal OAM is an origin-independent angular momentum of a light beam that can be associated with a helical or twisted wavefront. The external OAM is the origin-dependent angular momentum that can be obtained as cross product of the light beam position (center of the beam) and its total linear momentum.

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  1. D

    Square of x component of Orbital Angular momentum?

    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}...
  2. P

    3D harmonic oscillator orbital angular momentum

    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...
  3. O

    Sakurai page 196: Orbital angular momentum as rotation generator

    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...
  4. Einj

    Orbital angular momentum and powers of k

    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...
  5. J

    What is Orbital Angular Momentum?

    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...
  6. E

    Orbital angular momentum possible values of an electron in a hydrogen atom

    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...
  7. C

    Spin and Orbital Angular Momentum

    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...
  8. R

    Addition of orbital angular momentum in valence 4f^2 electronic configuration

    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...
  9. USeptim

    Wave function collapse by orbital angular momentum operator Lz

    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...
  10. W

    Orbital Angular Momentum Origin

    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...
  11. N

    [QM] spin and orbital angular momentum: most efficient method?

    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(...
  12. J

    Expectation Value of a component of Orbital Angular Momentum

    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
  13. U

    Measuring orbital angular momentum

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

    Calculate 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...
  15. G

    Exploring the Role of Orbital Angular Momentum in Atomic Structure

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

    Orbital angular momentum and kinetic energy

    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...
  17. P

    Orbital angular momentum of O2

    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...
  18. jinksys

    Orbital Angular Momentum of the Sun-Jupiter System

    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
  19. A

    Orbital angular momentum quantum number

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

    Accretion discs - Orbital angular momentum

    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...
  21. L

    Quick question about orbital angular momentum

    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...
  22. amarante

    Orbital Angular Momentum with eccentricity

    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...
  23. Amith2006

    Why is Orbital Angular Momentum Quantized in Quantum Mechanics?

    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...
  24. M

    Sun’s contribution to total orbital angular momentum of Sun-Jupiter orbit

    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...
  25. N

    Orbital angular momentum problem

    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...
  26. B

    Lunar Orbital Angular Momentum

    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...
  27. B

    Cancelation of electron orbital angular momentum

    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?
  28. LarryS

    Orbital Angular Momentum and Uncertainty?

    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...
  29. L

    Orbital angular momentum operator

    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...
  30. I

    Electron orbital angular momentum

    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...
  31. M

    What is L^2Ψ for a 3px state of a H-atom?

    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...
  32. S

    Angular momentum and orbital angular momentum problems

    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...
  33. J

    What Determines the Direction of Twist in Helical Wavefronts?

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