Orbital angular momentum Definition and 83 Threads
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.
The section Kepler’s Second Law here describes the above equation.
In this problem,
##\text{r = D, m = M and v = V}##
What is the way to go about finding out ##\theta## as shown in Figure 13.21?
I think that the quantum numbers are l=1 and ml=0, so I write the spherical harmonic Y=Squareroot(3/4pi)*cos(theta).
I would like to know how to compute the wave function at t=0, then I know it evolves with the time-evolution operator U(t), to answer the first request.
The classic way to go about this problem would be to use Kepler's laws and thus find the new time period of earth.
However I encountered this question in a test on rotational motion which deals with conservation of angular momentum.
The equation used here would be I1ω1= I2ω2
Replacing I with MR2...
Find the probability distributions of the orbital angular momentum variables ##L^{2}## and ##L_{z}## for the following orbital state functions:
##\Psi(x) = f(r) sin(\theta) cos(\theta)##
##\Psi(x) = f(r) cos^{2}(\theta)##I am aware that the prob. distribution of an observable is ##|<a_{n} |...
In this article it discusses the generation of something called super chiral light and claims with metamaterials they can make it have very high angular momentum like l=100. What does that really mean? How does that relate in magnitude to the normally computed linear momentum of a photon p=h/λ...
Consider the following experiment from the point-of-view of classical mechanics and classical electromagnetism: An originally free electron then passes through a magnetic field that is oriented so that it causes the electron to turn to, say, the right. During the “turning” of the electron (a...
This is a very special case.
In my 50 years studying physics I have never seen any discussion of photons having orbital angular momentum. Any angular momentum for photons in orbit around a black hole must be a GR question. I have not specialized in GR but I don’t recall any discussion of it.
I...
Hello,
I'm trying to calculate the measurement of the orbital angular momentum of the state l=1 and m = -1. The operator for the angular momentum squared is
## L^2 = -\hbar (\frac{1}{sin\theta}(\frac{\partial}{\partial \theta}(sin\theta\frac{\partial}{\partial \theta}))...
Hello,
I encountered the following statement in my lecture notes and there is a couple of things I don't understand:"Let's consider two particles with spins ##s_1 = \frac{1}{2}## and ## s_2 = 1## with a spherically symmetric interaction potential. Assume these two particles are in a two...
Hello,
in classical physics orbital angular momentum is defined as the cross product of the position vector 'r' and the momentum 'p'. A friend told me that all moving objects must have orbital angular momentum (even if it is moving along a straight line). That statement confuses me a lot...
Homework Statement
Gravitational force exerted on mass m is GMm/r^2
2. Relevant equations
Orbital velocity at distance R from Earth = ##\sqrt gR##
Escape velocity = ##\sqrt 2gR##
gR = GM/R
Fc = mV^2/R
F =m.aThe Attempt at a Solution
1) express acceleration of gravity in terms of G, M , and R...
Homework Statement
Homework EquationsThe Attempt at a Solution
Hi All,
My problem is that when I calculate this integral or use software to do it for me I get (3*i*pi)/16, when I've been told that the answer is 1/2i giving a probability of 1/4. Would someone be able to point out where my...
I'm trying to understand the rotations of rigid diatomic molecules such as HCl. My understanding of the orbital angular momentum is that it is quantized with a total value equal to
$$E=\frac{\hbar^2}{2I}J(J+1)$$
where I is the rotational moment of inertia and J is the quantum number. Also, J...
There are two types of angular momentum: orbital and spin. If we define their operators as pseudo-vectors \vec{L} and \vec{S}, then we can also define the total angular momentum operator \vec{J} = \vec{L}+\vec{S}.
Standard commutation relations will show that we can have simultaneous well...
A spiral phase plate can change the orbital angular momentum of a beam of light. Should I think of the beam of light carrying the orbital angular momentum or the photons that make up the beam light?
If the orbital angular momentum is carried by the individual photons what is being orbited, the...
Homework Statement
Consider an electron in a state described by angular wavefunction $$\psi(\theta,\phi)=\sqrt{\frac{3}{4 \pi}}\sin \theta \cos \phi$$ Here θ and φ are the polar and azimuthal angles, respectively, in the spherical coordinate system.
i. Calculate the probability that a...
I am trying to understand Wen and Zee's article on topological quantum numbers of Hall fluid on curved space: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.69.953
They passingly mentiond the fact that a spinning particle with orbital angular momentum $s$ moving on a manifold with...
Is the wavefront velocity if an OAM mode 1 light beam proportional to its wavelength?
I understand that the helical structure step length gives the wavelength of the beam. In this case, a small wavelength beam would travel much slower. The problem is, f=v/λ, but now v<c and if λ is shorter then...
It is known that particles with rest mass cannot travel at the speed of light.
Can we also say that particles that travel at subliminal velocity, like these OAM photons do, have mass?
It has been demonstrated [1] that these beams can be thought as made of photons that posses intrinsic OAM, and...
Homework Statement
A stationary, axisymmetric, spacetime has two Killing vector fields [ξt, ξφ] corresponding to translation along t or φ directions. A particle of unit mass moving in this spacetime has a four-velocity u = γ[ξt + Ωξφ].
(i) Explain why we can interpret this as a particle moving...
Homework Statement
A hydrogen atom is in the 3d state. Determine the orbital angular momentum.
Homework Equations
unnecessary
The Attempt at a Solution
I already know how to figure this out and have an answer but WHAT ARE the units?! It's not kgm/s^2!
Hello.
Here, I'm asking why total orbital quantum number l and total magnetic quantum number m are zero for closed subshell in atom.
Let me review the addition of angular momentum first: Each electron has its own orbital quantum number li and magnetic quantum number mi. Then for two electrons...
One of the best explanations of orbital angular momentum for the electron comes from Dirac himself. At around 39:30 of this youtube video (you will need headphones, but it is well worth it), Dirac talks about the non-commutation of operators, how quantum mechanics is more general then classical...
Recently I've been studying Angular Momentum in Quantum Mechanics and I have a doubt about the eigenstates of orbital angular momentum in the position representation and the relation to the spherical harmonics. First of all, we consider the angular momentum operators L^2 and L_z. We know that...
Homework Statement
Find the energy levels of a spin ##s=\frac{3}{2}## particle whose Hamiltonian is given by:
##\hat{H}=\frac{a_1}{\hbar^2}(\hat{S}^2-\hat{S}_x^2-\hat{S}_y^2)-\frac{a_2}{\hbar}\hat{S}_z## where ##a_1## and ##a_2## are constants.
Homework Equations
In the ##\hat{S}_z## basis...
Starting with the orbital angular momentum of the ith element of mass, $ \vec{L}_I = \vec{r}_I \times \vec{p}_I = m_i \vec{r}_i \times \left( \omega \times \vec{r}_i\right) $, derive the inertia matrix such that
$\vec{L} =I\omega, |\vec{L} \rangle = I |\vec{\omega} \rangle $
I used a X b X c...
I'll start with this question, how much "mass" does something have to have before centrifugal force exceeds gravity on earth?
I used basic physics of centrifugal force and gravity, used force vectors, and the math doesn't jive. This is what I mean.
There are 2 forces on Earth that everything...
I've been tutoring for chemistry and someone asked me to clarify the difference of spin angular momentum and orbital angular momentum without math.
I was trying to think of a metaphor, but I wanted to make sure it's a fair one--the spin angular momentum is like Earth rotating on its own axis...
The definition of orbital angular momentum, whether for classical mechanics or for quantum mechanical operators, is rxp. Technically, according to this definition, one particle can possesses orbital angular momentum - in this case about the origin.
But I cannot think of any examples, in...
So a particle has intrinsic parity ##\pm 1 ## .
The parity of a system of particles is given by product of intrinsic parities and the result is: ##(-1)^l ## (1).
Questions:
1) How does this result follow?
and what exactly is ##l## here? so it's the orbital angular momentum, so say a particle...
Homework Statement
Show that for hydrogen the matrix element <2 0 0|z|2 1 0> = -3a0 where a0 is the Bohr Radius.
On account of the non-zero value of this matrix element, when an electric field is applied to a hydrogen
atom in its first excited state, the atom's energy is linear in the field...
Homework Statement
Verify by brute force that the three functions cos(θ), sin(θ)eiφ and sin(θ)e−iφ are all eigenfunctions of L2 and Lz.
Homework Equations
I know that Lz = -iћ(∂/∂φ)
I also know that an eigenfunction of an operator if, when the operator acts, it leaves the function unchanged...
When we first learn of selection rules for atomic transitions, we learn that electrons have to change between states that differ in angular momentum by at most 1ħ, because photons have 1 unit of spin angular momentum.
However, photons can have arbitrarily high integer quantities of orbital...
I read this article, and I'm confused about several things.
http://scitation.aip.org/content/aip/magazine/physicstoday/article/57/5/10.1063/1.1768672
Apparently, light can have orbital angular momentum as well as spin. But I don't see how this is possible, at least in vacuum. Is this in vacuum...
Just a quick question on photon orbital angular momentum.
In the equation for photon energy: E2 = p2c2 + m2c4
Is OAM counted in the p2c2 part? Or does the above equation only apply to photons with normal momentum and there is another term for the angular momentum?
The normal relation for p...
Homework Statement
We have the initial orbital angular momentum state in the x basis as |l,ml>x=|1,1>x. We are asked to find the column vector in the z-basis that represents the initial orbital angular momentum of the above state. It then says "hint: use an eigenvalue equation".
Homework...
Suppose I have particle in three dimensional space whose position space wavefunction in spherical coordinates is ##\psi(r,\theta,\phi)##. The spherical harmonics ##Y_{\ell,m}## are a complete set of functions on the 2-sphere and so any function ##f(\theta,\phi)## can be expanded as...
Homework Statement
Consider the case of an atom with two unpaired electrons, both of which are in s-orbitals. Write the full basis of angular momentum eigenstates representing the coupled and uncoupled representations
Homework Equations
l=r×p
lx=ypz-zpy
ly=zpx-xpz
lz=xpy-ypx
l+=lx+ily...
Amazed by the closeness of equations for orbital angular momentum L and spin angular momentum S, I can't help asking is associated Legendre differential equation involved in solving spin function? I only heard that spin naturally comes from treatment of quantum mechanics with relativity theory...
Hi, I have a question related to the orbital angular momentum.
In the referring to Arfken & Weber Mathematical Methods for physicists-6th edition page 267,
"In the relativistic Dirac equation, orbital angular momentum is no longer conserved, but J=L+S is conserved,"
Here, I want to...
In particle physics we know that total angular momentum is conserved and its equal to orbital angular momentum plus spin angular momentum Can you give an example for me this total angular momentum conservation with explain specificly tell orbital angular momentum and spin angular momentum.
How to prove when electron spin is perpendicular to linear momentum, orbital angular momentum can't be 0.
And when they are paralleled, orbital angular momentum is 0.
Thanks.
So, I've been looking into orbital angular momentum and magnetic moments, (which, at least in normal space with a normal angular topology seems limited to integer values of spin). (My model so far has been a parabolic potential harmonic oscillator in 3d, and the sort of spinning modes you can...
"Locally, the spin density S is an intrinsic (i.e. origin-independent) quantity, which is associated with the local ellipticity of the polarization of light. In turn, the orbital AM density L=r x P0 is a manifestly extrinsic (origin-dependent) and is produced by the corresponding canonical...
Homework Statement
Taken from Binney's Text, pg 143.
Homework Equations
The Attempt at a Solution
From equation (7.36): we see that ##\delta a## is in the direction of the angle rotated, ##\vec{x}## is the position vector, and ##\vec{n}## is the unit normal to the plane of...
Homework Statement
A hydrogen atom is identified as being in a state with n=4. What is the magnitude of the total orbital angular momentum for the largest permitted value of l?
Homework Equations
n>l, l is bigger or equal to m
The Attempt at a Solution
The allowed l= 3,2,1
The allowed m for...
Homework Statement
Consider an electron with spin \frac{1}{2} and orbital angular momentum l=1. Write down all possible total angular momentum states as a combination of the product states | l=1 , m_l > | s = \frac{1}{2} , m_s >
Homework Equations
Lowering operator : J_- |j, m> =...
Homework Statement
If a particle has spin 1/2 and is in a state with orbital angular momentum L, there are two basis states with total z-component of angular momentum m*hbar l L,s,Lz,sz > which can be expressed in terms of the individual states ( l L,s,Lz,sz > = l L,Lz > l s,sz > ) as
l...