# Tagged Questions

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### Why does the raising and lowering operator not affect total angular momentum?

My notes define: $$L_{\pm} = L_{x} \pm i L_{y}$$ and states: $$[L_{z},L_{\pm}] = \pm \hbar L_{\pm}$$ I'm fine with this as it's easy to show the result with some ugly algebra. It then says: ...
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I want to work out the maximum and minimum values for $m_{\ell}$. I know that $\lambda \geq m_{\ell}$, therefore $m_{\ell}$ is bounded. In the lectures notes there is the following assumption: $$... 1answer 124 views ### What is the Weyl algebra of a confined bosonic particle? The abstract Weyl Algebra W_n is the *-algebra generated by a family of elements U(u),V(v) with u,v\in\mathbb{R}^n such that (Weyl relations)$$U(u)V(v)=V(v)U(u)e^{i u\cdot v}\ \ Commutation\ ...
In Holstein-Primakoff and Dyson-Maleev representation, spin operators are represented by bosonic operators. Roughly speaking, a state with $S^z=S-m$ corresponds to a state containing $m$ bosons. In ...
### 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? ...