For a System With 2 Particles

For a system of I particles → (m_{s1}=\frac{+\frac{1}{2}},\frac{-1}{2}) , [S_{1}=\frac{1}{2}] (m_{s2}=\frac{+\frac{1}{2}},\frac{-1}{2}) , [S_{2}=\frac{1}{2}] (\zeta=|S_{1}+S_{2}|\cdot---|S_{1}+S_{2}|) with diff. of Unity. 0, 1 for (p=0) (m_{s}=0) , (m_{s}=+1,0,-1) , fer (s=1) |s_{i},m_{s}>=\sqrt{|\frac{1}{2},+\frac{1}{2}>&=&\int|4\rangle\ |\frac{1}{2},-\frac{1}{2}\rangle&|4\rangle\ |\frac{1}{2}\rangle&|4\rangle\ \end{matrix}|4\rangle] |s₂, MB₂>=21½> = $11> |s, ms> = |0, 0>, S=0 Singlet |1, +1>, |1, 0>, |1, -1> for s=1 Triplet |s, ms> = or |s1, ms1> |s2, ms2> |s, ms>= |s1, s2; ms1, ms2> or |s, ms) = |ms1, ms2> The content appears to be related to quantum mechanics, specifically calculations involving the coupling of two angular momenta. The text is written in black ink on white paper. There are no visible drawings or diagrams. The writing is relatively neat, though some characters might be difficult to interpret accurately due to handwriting variations. The content appears to be related to quantum mechanics, specifically calculations involving the coupling of two angular momenta. The text is written in black ink on white paper. There are no visible drawings or diagrams. The writing is relatively neat, though some characters might be difficult to interpret accurately due to handwriting variations. The minimum energy of the system→ [E=\alpha lt_{0}+2\epsilon_{1}+\epsilon_{2}] [=\alpha\times\frac{1}{2}\hbar w+2\times\frac{3}{2}\hbar w+\frac{5}{2}\hbar w] [=\frac{j^{3}}{2}\hbar w] \[(opd\%n-b)\] [\frac{uej.6}{age-81}] \[E_{n}=\frac{\eta^{2}\pi^{2}\hbar^{2}}{\alpha^{8}mL^{2}}\] \[\eta=1,2,3\cdot-\] \[\epsilon_{i}=\frac{\pi^{2}\hbar^{2}}{\alpha mi^{2}}=\alpha e~v\] \[n=3\] $ \[m=2\] \[E=\alpha~\epsilon_{1}+\epsilon_{2}\] \[n=1\] [E=-\alpha x\frac{\pi^{2}\hbar^{2}}{2mi^{2}}+4\frac{\pi^{2}\hbar^{2}}{2mi^{2}}] [E=2x\frac{\pi^{2}\hbar^{2}}{8mc^{2}}+2x\frac{4~\pi^{2}\hbar^{2}}{9mc^{2}}] [=\frac{1}{2}(\frac{\pi^{2}\hbar^{2}}{2m\iota^{2}})+2\times(\frac{\pi^{2}\hbar^{2}}{2m\iota^{2}})] [=\frac{1}{\alpha}(\frac{\epsilon_{0}}{2})+\alpha(\frac{\xi_{0}}{2})] [=\frac{5}{4}E_{0}] (ophon-b) The content appears to be related to some form of mathematical formula or equation involving variables represented by 'V', 'r', 's', and possibly others. The text is written in black ink on white paper. There are no visible drawings or diagrams. The writing is relatively neat, though some characters might be difficult to interpret accurately due to handwriting variations. for Triplet [g=1] [S_{j}=\frac{1}{2}=S_{2}] If = S= (option-1) (\beta=0\rightarrow\int\vec{\sigma_{1}}.\vec{\sigma_{2}}=-3) ; 18=1, (\vec{\sigma_{2}}=1) [\dot{\vec{S}{i}}:\vec{S}{2}}=\frac{\hbar^{2}}{4}\rightarrow v(r)=\frac{i}{4}v_{b}(\gamma)]