Timeline for Eigenvalues of basis change matrix for angular momentum
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 7, 2021 at 2:07 | answer | added | ZeroTheHero | timeline score: 2 | |
| Mar 7, 2021 at 1:13 | comment | added | Cosmas Zachos | Nothing deep: the kernel expands, becomes bigger, as the dimensionality of the matrix becomes bigger. The transposes of (1,....,-1), (0,1,...,-1,0), (0,0,1,...,-1,0,0) .... are the null vectors, an ever expanding set... | |
| Mar 7, 2021 at 1:10 | comment | added | IchKenneDeinenNamen | Thanks for the suggestions! I may ask the question on Math SE indeed. In fact, I found this question thanks to your remark: math.stackexchange.com/questions/279445/… which may have some interesting elements. However, could you explain what you mean by "expanding kernel" in your last comment? I'm not familiar with this specific term in the context. | |
| Mar 6, 2021 at 23:58 | comment | added | Cosmas Zachos | Actually the structure is better than bisymmetric. There is symmetry across the perpendicular and horizontal that go trough the center. That readily displays the expanding kernel. | |
| Mar 6, 2021 at 22:33 | comment | added | Cosmas Zachos | Your A is a bisymmetric matrix. You might ask in MSE about those... They have really special properties... | |
| Mar 6, 2021 at 22:20 | comment | added | Cosmas Zachos | ...and j+1/2 for half-integer spins. This is plausible from the bisymmetric structure... | |
| Mar 6, 2021 at 16:58 | comment | added | IchKenneDeinenNamen | Hi @CosmasZachos, for j = 2, 0.375 is another eigenvalue and for j = 3, you also get 0.3125. As for the kernel, I can conjecture it has dimension j for integer j. | |
| Mar 6, 2021 at 16:45 | comment | added | Cosmas Zachos | No ideas. Indeed, squaring the elements of the orthogonal matrices $d^j_{m~m'}(\pi/2)$ is the way to explore the numerics. Note for j=3/2 the eigenvalues 1 and -1/2 persist, but the kernel has increased to two null vectors... As j increases the rank of A decreases dramatically. You claim you've found different eigenvalues for j=2? | |
| Mar 5, 2021 at 22:30 | history | asked | IchKenneDeinenNamen | CC BY-SA 4.0 |