What is total angular momentum: Definition and 64 Discussions
In quantum mechanics, the total angular momentum quantum number parametrises the total angular momentum of a given particle, by combining its orbital angular momentum and its intrinsic angular momentum (i.e., its spin).
If s is the particle's spin angular momentum and ℓ its orbital angular momentum vector, the total angular momentum j is
The associated quantum number is the main total angular momentum quantum number j. It can take the following range of values, jumping only in integer steps:
where ℓ is the azimuthal quantum number (parameterizing the orbital angular momentum) and s is the spin quantum number (parameterizing the spin).
The relation between the total angular momentum vector j and the total angular momentum quantum number j is given by the usual relation (see angular momentum quantum number)
The vector's z-projection is given by
where mj is the secondary total angular momentum quantum number, and the
ℏ
{\displaystyle \hbar }
is the reduced Planck's constant. It ranges from −j to +j in steps of one. This generates 2j + 1 different values of mj.
The total angular momentum corresponds to the Casimir invariant of the Lie algebra so(3) of the three-dimensional rotation group.
assume that we have N spin-1 bosons all on the same spatial orbit.
The problem is that what values the total angular momentum can be?
I am puzzled by this problem for a long time
maybe a bit permutation group theory is needed?
i guess this type of problem is well solved
Is there...
assume that we have N spin-1 bosons all on the same spatial orbit.
The problem is that what values the total angular momentum can be?
I am puzzled by this problem for a long time
maybe a bit permutation group theory is needed?
i guess this type of problem is well solved
Is there...
Question:
A woman with a mass of 55.0 is standing on the rim of a large disk that is rotating at an angular velocity of 0.550 about an axis through its center. The disk has a mass of 106 and a radius of 4.10 .
a.)Calculate the magnitude of the total angular momentum of the...
An electron in a hydrogen atom occupies the combined position and spin state.
\Psi\left(\vec{r},\xi\right)=\left(\sqrt{1/3}Y^{1}_{0}\xi_{+}+\sqrt{2/3}Y^{1}_{1}\xi_{-}\right)
What are the possible measured values of J^{2} (where J is the total angular momentum of the electron L + S) and...
Hello I just can't seem to get this problem right
Homework Statement
The hour and minute hands of Big Ben in London are 2.6 m and 4.58 m long and have masses of 68.6 kg and 97 kg respectively. Calculate the total angular momentum of the minute and hour hand about the center point. Treat...
lets say there is an electron configuraiton of 1s^2 2s^2 2p^2 3p^1
I want to find the total angular momentum quantum number, J=L+S
considering the n=1 state, there are two electrons, in the s shell which means one is spin 1/2 and the other is spin -1/2 giving a total spin of 0. The s shell...
lets say there is an electron configuraiton of 1s^2 2s^2 2p^2 3p^1
I want to find the total angular momentum quantum number, J=L+S
considering the n=1 state, there are two electrons, in the s shell which means one is spin 1/2 and the other is spin -1/2 giving a total spin of 0. The s shell...
Hi,
How does one find the s=0 state for the addition of the spin of 4 (for example) electrons?
More generally, how does one obtain the total spin of 4 electrons?
I understand that for 2 electrons one can read the s=1 and s=0 states from a table of Clebsch-Gordan coefficients.
Homework Statement
A dumbbell consists of two small balls attached to the ends of a 1.0m rod of negligible mass. Ball1 has a mass of 1.0kg and ball2 has a mass of 3.0kg. The dumbbell rotates about a fixed vertical axis midway between the balls, with an angular speed of 1/pi rev/s. What is the...
Homework Statement
Consider the 6g state of an electron in a hydrogen atom.
Enter the smallest possible value of the total angular momentum quantum number.
Homework Equations
hund's rules:
1. the total spin angular momentum S should be maximized to the extent possible without...
hey everyone, I've been working through a past paper and I'm stuck on a question:
"(a) Consider a system consisting of n distinct particles P1, P2, : : :, Pn, with masses m1, m2, ..., mn and position vectors r1, r2, : : :, rn, relative to the origin O of an inertial frame, respectively...
Two lightweight rods d = 23 cm are mounted perpendicular to an axle and at 180° to each other. (Fig. 11-24). At the end of each rod is a 700 g mass. The rods are spaced 40 cm apart along the axle. The axle rotates at 41 rad/s.
http://www.geocities.com/sinceury/11-24alt.gif
(a) What is...
This is a problem that seemed easy to me. I keep recalculating the answer, and I keep getting it wrong. I'm not sure if I'm approaching the problem incorrectly, or if I'm just making some small dumb mistake. Here's the question:
Big Ben (see the figure below), the Parliament Building...
Who knows the formula to calculate the eigenvalues of total angular momentum between two different states? In particular, what is the matrix element of
<S, L, J, M_J | J^2 | S', L', J', M'_J> ?
Thank's...