# Tagged Questions

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### Possible Error in deriving conformal generator

My professor gave me the following derivation for the full generator of the Lorentz transformations. The starting point is to consider a subgroup of the conformal group that leaves the origin fixed ...
I know that different representations of this algebra correspond to different spin. One can sort the representation according to the casimir. For any simple Lie algebra, the operator $$T^2 = ... 1answer 170 views ### How to theoretically determine the angular momentum of an atom? To determine if an atom is a boson or a fermion I have to count the fermions that constitute the atom (protons, neutrons and electrons). My question is: How to theoretically (as opposed to ... 2answers 175 views ### Problem counting spin states I can't figure out how many different spin states I can create with a four-electron system. I think I can create a spin-zero state, three spin-one states, and five spin-two states. That gives me nine ... 2answers 438 views ### In quantum mechanics(QM), can we define a high-dimensional “spin” angular momentum other than the ordinary 3D one? Inspired by my previous question Questions about angular momentum and 3-dimensional(3D) space? and another relevant question How to define angular momentum in other than three dimensions? , now I get ... 3answers 381 views ### Quantum mechanical angular momentum and spin formalism/notation I am currently stuck on the following notation: \frac{1}{2}\otimes\frac{1}{2} = 0 \text{ (antisym) } \oplus 1 \text{ (sym) } No matter what I tried, I couldn't derive the identity. I am sure that ... 3answers 406 views ### The Asymmetry between Real and Imaginary in the three Pauli Spin Matrices The Pauli spin matrices$$ \sigma_1 ~=~ (\begin{smallmatrix} 0 & 1 \\ 1 & 0 \end{smallmatrix}), \qquad\qquad \sigma_2 ~=~ (\begin{smallmatrix} 0 & -i \\ i & 0 ...
I understand how spin is defined in analogy with orbital angular momentum. But why must electron spin have magnetic quantum numbers $m_s=\pm \frac{1}{2}$ ? Sure, it has to have two values in ...