Tagged Questions
1
vote
1answer
90 views
Can 3 photons be combined to give a spin-0 projection?
Motivation: The neutral pion decays to 2 photons ($\pi^0\to\gamma\gamma$) most of the time. For the decay of the neutral to 3 photons ($\pi^0\to 3\gamma$) we have an upper limit on the branching ...
2
votes
2answers
148 views
In quantum mechanics(QM), can we define a high-dimensional “spin” angular momentum other than the ordinary 3D one?
Inspired by my previous question Questions about angular momentum and 3-dimensional(3D) space? and another relevant question How to define angular momentum in other than three dimensions? , now I get ...
2
votes
1answer
105 views
Questions about angular momentum and 3-dimensional(3D) space?
Q1: As we know, in classical mechanics(CM), according to Noether's theorem, there is always one conserved quantity corresponding to one particular symmetry. Now consider a classical system in a $n$ ...
4
votes
2answers
182 views
Why must the angular part of the Schrodinger Equation be an eigenfunction of L^2?
I was reading about the solution to the Schrodinger Equation in spherical coordinates with a radially symmetric potential, $V(r)$, and the book split the wavefunction into two parts: an angular part ...
4
votes
2answers
86 views
quantization of angular momentum
What is the most direct way of observation of quantization of angular momentum?
0
votes
1answer
59 views
Angular Momentum Addition Theorem
If I have, for example a particle with $s = 3/2$ and $\ell = 2$, what are the allowed values of $j$?
I'm slightly confused because I know that $j = \ell + s$, so surely there is only one allowed ...
2
votes
2answers
121 views
Quantization of orbital angular momentum
Probably a very simple question, but I can't find the answer on the Internet.
I know nearly to nothing about quantum mechanics, but in statistical physics I'm confronted with the idea that the orbital ...
2
votes
1answer
104 views
Conservation of Angular momentum in the dipole selection rules
If the total angular momentum J of an atom is not changing during a dipole transition, where does the angular momentum for the photon come from?
4
votes
2answers
337 views
Quantum Mechanics: Show that the expectation value of angular momentum does not change with time
The potential is given by $V\left(\left\|(x,y,z)\right\|\right)$, so $[\hat{L}, \hat{H}] = 0$.
Using the definition of $\langle \hat{L} \rangle$ and the time-dependent Schrödinger equation, show that ...
2
votes
0answers
139 views
How is parity relevant to determining angular momentum?
Question:
Particle A, whose spin $\mathbf{J}$ is less than 2, decays into two identical spin-1/2 particles of type B.
What are the allowed values of the orbital angular momentum $\mathbf{L}$, ...
3
votes
2answers
129 views
Space Quantization of Quantum Angular Momentum
I am trying to understand what my book is trying to convey.
Quantum angular momentum is $L_z = m_l \hbar$
"Choosing arbitrarily a z axis and using an appropriate experimental technique, we measure ...
2
votes
2answers
145 views
A universe of angular momentum?
I read this on Wikipedia:
[...] That most tangible way of expressing the essence of quantum mechanics
is that we live in a universe of quantized angular momentum and the
Planck constant is the ...
1
vote
2answers
109 views
Spin of a particle and spin quantum number [duplicate]
what actually does the spin quantum number of a particle describe about? What it means when we say photon has spin 1, Higgs boson has spin 0, etc..?? What actually does that numerical value explain? I ...
3
votes
1answer
90 views
Mathematically, how do we deduce that angular momentum is bounded?
So, how do we know $J_{+}|j,(m=j)\rangle =|0\rangle$?
I.e. that m is bounded by j.
We know that $J_{+}|j,(m=j)\rangle =C|j, j+1\rangle$, but how do I know that gives zero? Is it by looking at its ...
1
vote
0answers
97 views
How is multiplicity given by 2S+1?
Suppose there are two electrons in an atom with $s_1 = \frac{1}{2}, l_1 = 1$ and $s2 = \frac{1}{2}, l_2 = 1$. Hence the total $S$ (of the atom) may be +1 or 0. And total $L$ is either +2,+1 or 0.
Now ...
0
votes
0answers
43 views
What exactly is the spin of a particle? [duplicate]
Possible Duplicate:
What is spin as it relates to subatomic particles?
I'm having a hard time grasping the concept of spin, my textbook describes it very vaguely:
Stable matter contains ...
1
vote
1answer
251 views
How do I find the eigenvalues for the angular momentum ladder operators?
I am trying to calculate the normalising constants for the angular momentum ladder operators but am stuck when I need to calculate expected values.
How can I find the expected values
1
vote
1answer
104 views
What do the $j$ and $m$ stand for in $|j,m\rangle$ for angular momentum in quantum mechanics?
I'm assuming it is a jth state with m value as total angular momentum?
3
votes
3answers
200 views
Quantum mechanical angular momentum and spin formalism/notation
I am currently stuck on the following notation:
$\frac{1}{2}\otimes\frac{1}{2} = 0 \text{ (antisym) } \oplus 1 \text{ (sym) }$
No matter what I tried, I couldn't derive the identity. I am sure that ...
2
votes
2answers
215 views
Why for a spin half particle, possible outcomes of measuring spin projection along any direction are the same?
If one measures the projection of spin of a spin half particle along the x axis one will always get plus or minus half $\hbar$
Measuring it along the y axis one will always get plus or minus half ...
7
votes
1answer
268 views
Classical vs. Quantum use of the spin 4-vector
I have a few basic questions about the Pauli-Lubanski spin 4-vector S.
I've used it in quantum mechanical calculations as an operator, that is to say each of the components of S is a matrix operator ...
1
vote
2answers
205 views
Angular Momentum Operators Non-Degenerate
Typically one writes simultaneous eigenstates of the angular momentum operators $J_3$ and $J^2$ as $|j,m\rangle$, where
$$J^2|j,m\rangle = \hbar^2 j(j+1)|j,m\rangle$$
$$J_3 |j,m\rangle = \hbar ...
1
vote
1answer
98 views
Commutation relation of $J^2$ and $R(\alpha,\beta,\gamma)$
If $R(\alpha,\beta,\gamma)$ is the Rotation operator and $\alpha,\beta,\gamma$ are Euler angles and $J$ is the total angular momentum then how to get to this:
$$[J^2,R]~=~0?$$
This is stated in ...
2
votes
2answers
287 views
Question on Total, Orbital and Spin Angular momentum
I am reading about the total, orbital and spin angular momentum, and I am not clear as to what these generators actually do after exponentiating.
Could you give me a physical picture of what happens ...
-1
votes
1answer
84 views
Implications of rotational invariance
The state
$$|\psi\rangle ={1\over \sqrt 2}(|+\rangle|-\rangle-|-\rangle|+\rangle)$$
of system made up of 2 spin-$1\over 2$ particles is invariant under the operator
$$\exp{i\theta S_y}.$$
What ...
2
votes
0answers
123 views
Angular momentum confusion
Could somebody please explain what is going on here?
We have a system of two indistinguishable spin-1 bosons. We shall adopt the center of mass frame.
Let
$S$ = total spin
$L$ = relative orbital ...
3
votes
0answers
116 views
What is the Landé g factor?
What is the Landé g factor?
I know that it gives the relation between magnetic moment and angular moment, but i wanted to know why are those magnitudes related to each other and why is the magnetic ...
1
vote
0answers
46 views
Wigner $3j$ symbols
I am trying to determine the expansion that requires using $3j$ symbols; however, I am running into some conceptual snags. First, the expansion produces symbols that have m's that do not agree with ...
2
votes
1answer
318 views
What is the spin rotation operator for spin > 1/2?
For spin $\frac{1}{2}$, the spin rotation operator $R_\alpha(\textbf{n})=\exp(-i\frac{\alpha}{2}\vec{\sigma}\cdot\textbf{n})$ has a simple form:
...
1
vote
2answers
188 views
How to write Schrodinger equation when a particle with some spin quantity and orbital angular momentum
Quantum mechanics: Suppose that there is a particle with orbital angular momentum $|L|$. But the particle also has spin quantity $|S|$. The question is, how do I reflect this into Schrodinger ...
3
votes
3answers
142 views
What is predicted to happen for electron beams in the Stern-Gerlach experiment?
The Stern–Gerlach experiment has been carried out for silver and hydrogen atoms, with the result that the beams are deflected discretely rather than continuously by an inhomogenous magnetic field. ...
2
votes
1answer
113 views
Normalization of a spin-like quantity in matrix mechanics
Suppose that there is a quantity in Heisenberg picture as the following:
$A=u_1\Sigma_1 + u_2\Sigma_2 +u_3\Sigma_3$
I am not sure why $u_1,u_2,u_3$ is normalized to be ${u_1}^2 + {u_2}^2 + {u_3}^2 ...
3
votes
1answer
112 views
Determining the spin of wavefunction
We all know that by uncertainty principle, location of a wave-particle is perfectly determined when uncertainty of momentum becomes infinite. (I also heard that in reality, it is almost impossible to ...
2
votes
2answers
147 views
Multiplicity of eigenvalues of angular momentum
Reading Dirac's Principles of Quantum Mechanics, I encounter in § 36 (Properties of angular momentum) this fragment:
This is for a dynamical system with two angular momenta $\mathbf{m}_1$ and ...
4
votes
2answers
729 views
Why Silver atoms were used in Stern-Gerlach experiment?
For the Stern-Gerlach experiment done in 1922:
1-why silver atoms were used?
2-Silver atom contains many electrons in different orbits (different $l$'s). Wouldn't the inner -shell electrons be ...
3
votes
2answers
289 views
How is angular momentum measured in experiments/in practice? [duplicate]
Possible Duplicate:
How does one experimentally determine chirality, helicity and spin?
How do you find spin of a particle from experimental data?
We read about and study angular momentum ...
1
vote
2answers
106 views
Why isn't the maximum eigenvalue of $J_z$ squared equal to the maximum eigenvalue of $J^2$?
During a standard derivation of the eigenvalues of the angular momentum operators, $J^2$ and $J_z$, where
$$J^2|\alpha, \beta\rangle =\hbar^2\alpha|\alpha, \beta\rangle$$
and
$$J_z|\alpha, ...
1
vote
2answers
275 views
what does it mean for a particle with no size to have angular momenta?
I recently was reading about higgs boson and particle spin recently and I stubble upon an question that contains an answer to what a spin is.
It explains that electrons etc. have no size yet they ...
2
votes
1answer
395 views
What does it really mean that particle has a spin of up/down? And how is spin actually meassured?
I been reading some physics articles (related to the recent discovery of the particle that could be a Higgs boson) posted online and it was talking about electron spin and how it can only have values ...
5
votes
3answers
396 views
Why does spin have a discrete spectrum?
Why is it that unlike other quantum properties such as momentum and velocity, which usually are given through (probabilistic) continuous values, spin has a (probabilistic) discrete spectrum?
10
votes
3answers
831 views
Adding 3 electron spins
I've learned how to add two 1/2-spins, which you can do with C-G-coefficients. There are 4 states (one singlet, three triplet states). States are symmetric or antisymmetric and the quantum numbers ...
3
votes
1answer
165 views
Why is there a phase factor when the two composite angular momentum is exchanged in Clebsch–Gordan coefficients
An identity exists for CG coefficients:
$$\langle j_1 m_1 j_2 m_2 |J M \rangle = (-1)^{j_1+j_2-J} \langle j_2 m_2 j_1 m_1|J M\rangle,$$
But why is there a phase factor $(-1)^{j_1+j_2-J}$?
It seems ...
3
votes
3answers
393 views
$\hbar$, the angular momentum and the action
Is there anything interesting to say about the fact that $\hbar$, the angular momentum and the action have the same units or is it a pure coincidence?
2
votes
1answer
980 views
Angular momentum operator and expectation values
I was reading some notes and it says that $\langle L_z^2\rangle=\langle L^2\rangle$ IFF the system is radially symmetric. I can see that in order that the LHS of the statement implies that $\langle ...
4
votes
1answer
122 views
Eigenvalue of $L_z$
In section 4.3 of Griffths' "Introduction to Quantum Mechanics", just below Figure 4.6, the sentence begins
Let $\hbar \ell$ be the eigenvalue of $L_z$ at this top rung...
Why is this valid? ...
2
votes
1answer
203 views
How could $\textbf{S}^2$ not be a multiple of the identity?
I'm self-studying quantum mechanics with Sakurai's book (Modern Quantum Mechanics, 2nd edition) and came across the following in reference to the operator $\textbf{S}^2$:
As will be shown in ...
0
votes
1answer
319 views
Probability of getting a particular spin
I'm a beginner in quantum mechanics, and I'm a bit confused about states and the probability to measure certain values. I would like to understand at least the following simplified situation:
...
3
votes
1answer
251 views
Angular Momentum Addition Theorem - Sanity Check
Looking back at my quantum mechanics notes, the angular momentum addition theorem is listed as:
$j=j_1+j_2,j_1+j_2-1, ..., |j_1-j_2| $ (Using conventional notation)
, but I'm a little unsure how to ...
4
votes
1answer
328 views
Is all angular momentum quantized?
Angular momentum is definitely quantized in elementary particles and electrons in atoms.
Molecules also have characteristic rotation spectra.
Is it true that all angular momentum is quantized, ...
2
votes
1answer
478 views
General procedure for Clebsch-Gordan expansions
I'm wondering if the Clebsch-Gordan series generalize to any orthonormal set of basis functions? If so, how would one go about deriving an expression for an arbitrary set of basis functions (perhaps ...
