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Results tagged with quantum-spin
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user 206319
Fundamental characteristic property of particles which together with orbital angular momentum acts as the generator of rotations and which doesn't have a classical equivalent but is sometimes compared to and contrasted with classical intrinsic angular momentum.
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Why Consider Only Triplet States for Spin in $2$-Electron Systems?
I have a question regarding systems of 2 electrons and their spin properties. When the Hamiltonian of a system of 2 electrons can be written as a sum of two single-particle Hamiltonians that are ident …
- 1,978
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What is the meaning of the commutation relations (spin $1/2$ particles)?
I've often seen spin 1/2 commutation rules as a principle valid for every angular momentum. In some text books there is a derivation from symmetries principles.
My question is, if I have a spin $1/2$ …
- 1,978
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Is the number of spin states necessary in the density of states function?
I'm studying how to calculate the density of states in the final configuration in order to apply Fermi golden rule.
For free EM field the following expression is the starting point:
$$d^3n=\frac V {(2 …
- 1,978
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1
answer
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A particular representation of $SU(2)$ on $\mathbb R^3$
Studying physics I encounter group theory and it has told me that: the matrices that rotates $\mathbb R^3$ vectors in the Euclidean space are the representation of $SU(2)$. Namely, $SO(3)$ matrices ar …
- 1,978
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1
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Spin state rotations and spinors rotations
I've tried to do the calculations to derive the SU(2) matrices that rotates spinors from the rotation of the spin eigenstates.
The following is the procedure that I followed but at the end I didn't fi …
- 1,978
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2
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Are there two different spinors for the same spin state?
Let's say $ \begin{bmatrix} 1\\ 0\\ \end{bmatrix} $ and $ \begin{bmatrix} 0\\ 1\\ \end{bmatrix} $ are the eigenvector of $\hat S_z$, is the state $ -1\begin{bmatrix} 1\\ 0\\ \end{bmatrix} +0\begin{bm …
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Doubts about the use of tensor product In quantum mechanics
I'm studying quantum mechanic in particular tensor product and Hilbert space (for the first time).
I have some doubts and I would like to check if I have understood correctly.
Factorization
The stat …
- 1,978
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4
answers
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Spin of two identical particles
I read that when I have two identical particles with spin 1/2 there are 4 possibilities:
|↓↓⟩,|↑↑⟩,|↑↓⟩,|↓↑⟩.
Then since there is the symmetrization requirement I can take as eigenvalues the follow …
- 1,978
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Why can we factorize the state of a particle?
I read about factorization in these two cases:
When spin and position are not coupled it is
possible to factorize the state in a wave function and a spinor $|\psi\rangle|\chi\rangle$
If there are two …
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