Orbital Angular Momentum

#Orbital Angular momentum:- \[\vec{L}=\vec{\gamma}\times\vec{p}\] = x+y+ZR \[\vec{P}=P_{n}\hat{l}+P_{Y}\hat{j}+P_{z}\hat{R}\] \[\vec{L}=\iota_{n}\hat{i}+\iota_{y}\hat{J}+\iota_{z}\hat{R}\] [\vec{L}\times\vec{l}=(ln\hat{c}+l_{yj}+l_{z}\hat{k})\times(L_{x}\hat{l}+l_{yj}+l_{z}\hat{k})] [\mathcal{C}\times\hat{\mathcal{I}}=\hat{J}\times\hat{J}=\hat{R}\times\hat{R}=0] = LaLy R-LyLuk + Lットマーレzzy [+L_{x}L_{z}(-\hat{J})+L_{z}L_{x}\hat{J}] [=(L_{y}L_{z}-L_{z}L_{y})\hat{L}+(L_{z}L_{n}-L_{n}L_{z})\hat{J}] [+(L_{\pi}L_{y}-L_{y}L_{\eta})\hat{k}] [\vec{L}\times\vec{L}=[Ly,Lz]\hat{c}+[L_{z,L_{n}]\hat{j}+[L_{\lambda},L_{y}]\hat{k}] #Orbital Angular momentum:- \[\vec{L}=\vec{r}\times\vec{p}\] = x+y+ZR \[\vec{P}=P_{n}\hat{l}+P_{Y}\hat{j}+P_{z}\hat{R}\] \[\vec{L}=\iota_{n}\hat{i}+\iota_{y}\hat{J}+\iota_{z}\hat{R}\] [\vec{L}\times\vec{l}=(ln\hat{c}+l_{yj}+l_{z}\hat{k})\times(L_{x}\hat{l}+l_{yj}+l_{z}\hat{k})] [\mathcal{C}\times\hat{\mathcal{I}}=\hat{J}\times\hat{J}=\hat{R}\times\hat{R}=0] = LaLy R-LyLuk + Lットマーレzzy [+L_{x}L_{z}(-\hat{J})+L_{z}L_{x}\hat{J}] [=(L_{y}L_{z}-L_{z}L_{y})\hat{L}+(L_{z}L_{n}-L_{n}L_{z})\hat{J}] [+(L_{\pi}L_{y}-L_{y}L_{\eta})\hat{k}] [\vec{L}\times\vec{L}=[Ly,Lz]\hat{c}+[L_{z,L_{n}]\hat{j}+[L_{\lambda},L_{y}]\hat{k}] The equations involve variables such as P, M, Z, L, and Greek letters (possibly representing other variables or constants). There are no diagrams, symbols, or other elements besides the handwritten text. The handwriting is somewhat neat, with generally clear spacing between characters and lines. \[\vec{L}\times\vec{i}=i\hbar~L_{x}\tilde{i}+i\hbar~L_{4}\tilde{J}+i\hbar~L_{z}\tilde{k}\] \[=i\hbar(l_{\pi}i^{4}+i_{4}j^{\dagger}+i_{z}\hat{k})\] \[\vec{L}\times\vec{c}=i\hbar\vec{L}\}\ne0\] ⇒ ([^{[i,x]}=[(4p_{z}-z~p_{y}),x]) [=[yp_{z},x]-[zp_{y},x]] Q = \[[L_{4},y]=[(yp_{z}-zp_{4});y]\] \[=[YP_{z},Y]-[zP_{y},Y]\] \[=0-z[P_{y},y]-[z,y]P_{y}\] [[L_{n,1}y]=+i\hbar z] [Ly, y] = 0 \[[L_{x},x]=0\] \[[L_{n},y]=i\hbar z\] \[[L_{Y},z]=i\hbar\kappa\] \[\sqrt{L}_{n_{1}}zJ=-i\hbar~y\] \[[L_{y},\eta]=-i\hbar z\] [[\iota_{y},n]=-i\hbar~z] The equations involve variables such as L, x, y, z, p, and Greek letters (possibly representing other variables or constants). There are no diagrams, symbols, or other elements besides the handwritten text. The handwriting is neat and legible, with clear spacing between characters and lines.