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10
votes
6answers
742 views

What does vector operator for angular momentum measure?

Consider the vector operator for angular momentum $\hat L=\hat L_x \vec i +\hat L_y \vec j + \hat L_z \vec k$. Does this mean that if we want to measure the angular momentum of a particle in state $\...
1
vote
1answer
110 views

Why do we say spin/angular momentum is observable even though its components can't be determined simultaneously?

Why do we say spin or angular momentum of a particle is observable even though all of its components can't be determined simultaneously? For example, we can measure the $\hat{L_x}$ of a particle's ...
2
votes
1answer
60 views

Common eigenkets of spherically symmetric Hamiltonian

In a QM text it states: "Consider a spinless particle subjected to a spherical symmetrical potential. The wave equation is known to be separable coordinates, and the energy eigenfunctions can be ...
5
votes
1answer
205 views

Our choice of basis surely cannot effect possible outcomes of a measurement?

Common sense says that, of course, the outcome of a measurement on a quantum system cannot be affected by what base we choose to represent it in. However, while studying QM text, it seems like they ...
1
vote
0answers
86 views

How to measure $\mathbb{L}^2$ and $L_z $ simultaneously

What does an experiment look like, in which both quantities are measured simultanously?
10
votes
1answer
768 views

Sequential Stern-Gerlach devices - realizable experiment or teaching aid?

At least one textbook [1] uses sequential Stern-Gerlach devices to introduce to students that the components of angular momentum are incompatible observables. Viz., the $z$-up beam from a SG device ...
1
vote
3answers
2k views

Why is only one quantity of angular momentum i.e. $L_z$ quantized & not $L_x$ & $L_y$?

This is quoted from Arthur Beiser's Concepts of Modern Physics: Why is only one quantity of $\mathbf{L}$ quantized? The answer is related to the fact that $\mathbf{L}$ can never point in any ...
6
votes
2answers
3k views

Square of the Pauli matrices and the identity matrix

The square of any of the three Pauli Spin matrices is equal to the identity. Is there any physical meaning to this? Would you expect it? Maybe in the context of the $SU(2)$ group?
1
vote
2answers
182 views

How can $J_1^2, J_2^2, J_{1z}, J_{2z}$ commute mutually?

I'm reading through J. J. Sakurai's Modern Quantum Mechanics book and currently looking at the "Angular-momentum addition" part. Here, it says you have two options and that one option is to ...