University:
Santa Fe College
Course:
PHY 2048 | General Physics 1 with Calculus
Academic year:

2024
Views:

492

Pages:

6
Author:

Jabin F.

For one Particle \(\vec{J_{1}}=\vec{L}\) , \(\vec{J}_{2}=\vec{S}\) \(J_{I}=\mathcal{U}\) , \({J_{2}}^{\prime}=\beta\) ,mim2 For two perticles. \(J_{2}=.\vec{L}_{2}+\vec{S}_{2}\) , \(J_{2}=IJ_{2}+8_{2}1-...=IJ_{2}-S_{2}|\) \[\vec{J_{I}}=\vec{L_{I}}+\vec{S_{I}}\] \(\vec{J}=\vec{J}_{1}+\vec{J}_{2} J=|J_{1}+J_{2}|-\cdot\cdot\cdot|J_{1}-J_{2}|\) with diff-ofunity. Particles states [\vec{J}{z}=\vec{J}{1z}+\vec{J}{1z}] 1 (\dot{m}=-f{\neg}...+f}) with diff of Unity. J1,J2, M1, M2> or IJ1, mij J2m2> The content focuses on particle states, denoted by ket vectors with various indices. There is a mention of a system's state represented by ly,m>, and an equation involving inner products of states. The text is handwritten and somewhat cluttered, with equations distributed across the page. Σ=Jm>= 1 The content focuses on angular momentum coupling, Clebsch-Gordan coefficients, and transformations between different basis states. The text is handwritten and somewhat dense, with equations and symbols occupying most of the available space. |J1,m> |J1,J2| = C. G. Coefficient \[=\langle\vec{J}_{1},m_{1},\vec{J}_{2},m_{2}|\vec{J},m\rangle\] A Hermitian \(=<\vec{J}_{1z},m_{1z},\vec{J}_{2z},m_{2z}|\vec{J}_{z},m_{z}|\) ,m> \(\hat{A}|\phi\rangle=\lambda |\phi\rangle\) \[\langle\phi|\hat{A}=\langle\phi|\lambda\] ⇒ = ⇒ ((m-(m1+m2))=0) If m≠m₁+m₂ then = 0 (ii) If m = m₁+m₂, then ≠ 0 = [\sqrt{(J∓m)(J±m+1)}\hbar] (=\sqrt{(J₁∓m₁)(J₁±m₁+1)}\hbar] [+√{(J₂∓m₂)(J₂±m₂+1)}\hbar] = (-1)^(J₁+J₂-J) = (-1)^(J₁+J₂-J) = δ_J,J₁ δ_m,m₁ = √{(J±m+½)/(2J+1)} δ_m₁,m∓½ j = j₁ + j₂, m₁ = +j₁, m₂ = +j₂, m = m₁ + m₂ = j₁ + j₂ , = 1 J = j₁ + j₂, m₁ = -j₁, m₂ = -j₂, m = -j₁ - j₂ /J,J2;m,mz> [m_{i}=\pm\frac{1}{2}] The text is written in a cursive style, making it difficult to decipher the exact characters. The overall layout is simple, with the text centered on a blank background. J=1, m= +1 ..... then Cobweff. = 0- The content focuses on angular momentum, quantum states, and normalization conditions. The text is handwritten and somewhat messy, with equations scattered across the page. Some parts of the text are unclear or illegible, particularly in the last few lines. The image presents a single line of handwritten text, a mathematical equation representing a linear combination of two quantum states |ψ₁> and |ψ₂>. The coefficients of the linear combination are denoted as C₁ and C₂. The handwriting is clear and legible, with the equation centered on the page. The text is handwritten and somewhat messy, with equations scattered across the page. There seems to be an attempt at algebraic manipulations or calculations, but the meaning and purpose are unclear without additional information. The text is handwritten and somewhat messy, with equations scattered across the page. There seems to be an attempt at algebraic manipulations or calculations, but the meaning and purpose are unclear without additional information.