Physics Note - E-2=0

E₂ = 0 ⇒ 2 0 D 0 C 0 0 C2 = 0 0 0 0 0 0 0 0 \[3~e9_{0}E_{0}C_{2}\Rightarrow0\Rightarrow\{C_{2}=0\] -0 Normalisation Con \[|c_{1}|^{2}+|c_{2}|^{2}+|c_{3}|^{2}+|c_{4}|^{2}=0\] \[|c_{3}|^{2}+|c_{4}|^{2}=0\] if ( \({}_{3}=C_{4}\Rightarrow C_{3}=C_{4}=\frac{1}{\sqrt{2}}\) \[|\psi\rangle=\frac{1}{\sqrt{2}}(|211\rangle+|2|T\rangle)\] it C3-C4 \[|\psi\rangle=\frac{1}{\sqrt{2}}(|21|>-|21\overline{T}>)\] n=2 F= 4 fold deg. 12007, 12107,12117, 1219) without \[\frac{-13\cdot6}{4}+3e0_{0}F_{0}\] = \(\frac{-13\cdot6}{4}\) \[\frac{-136}{4}-3ea_{0}E_{0}\] In the presence of E.F. n=2 \(E_{2}=\int_{\frac{-i3\cdot6}{4}+3~ex_{0}E_{0}\\ 0\\ 0&D\\ \matrix}\) , 19247 1922), 19237 -13.6-3e9oEo→ 14217 4 \[|\phi_{21}\rangle=\frac{i}{\sqrt{2}}(|2.\circ\circ\rangle+|21\circ\rangle)\] \[|\phi_{22}\rangle=\frac{i}{\sqrt{2}}(|2||>+|2|\overline{\pi}\rangle)\] \[|\phi_{z,3}\rangle=\frac{1}{\sqrt{2}}(|^{2,|1\rangle-|2,|\overline{7}\rangle)\] \[|\phi_{z4}\rangle=\frac{1}{J^{2}}(1^{2~\circ\circ}>+|2~1\circ>)\] These are eisen in Corresponding to energy level. The image contains a handwritten page filled with mathematical equations. The equations are primarily focused on energy levels, denoted by E with various subscripts and parenthetical expressions. There are also numerical values, symbols, and conditions stated throughout the page. The overall layout is somewhat disorganized, with equations scattered across the page. The handwriting is generally legible, but some symbols and expressions are difficult to decipher due to the image quality and inconsistent notation. Image Analysis Image Content: The image contains handwritten mathematical equations and symbols. The text is written in black ink on a white background. The content is organized in multiple lines with consistent spacing. The equations are presented in a mix of inline and displayed formats. The overall appearance of the image is clean with clear handwriting. Transcribed Text: n_x = 1 n_y = 2 421 ψ_(12) = (2/a)sin(πn/a)sin(2πy/a) n_x = 2, n_y = 1 (22) ψ_(21) = (2/a)sin(2πn/a)sin(πy/a) 1Φ_nα> = 1/√2 |1,1>, |1,2> [H_(P_11) - E_2(′) H_(P_12) H_(P_21) H_(P_22) - E_2(′)] = 0 H_(P_11) = <φ_(21)|H_P|φ_(21)> H_(P_12) = <φ_(21)|H_P|φ_(22)> H_(P_22) = <φ_(22)|H_P|φ_(22)> H_(P_21) = <φ_(22)|H_P|φ_(21)> = (H_(P_12))^∗ H_(P_11) = ∫∫_(-∞)^(∞) φ_(21)^∗ H_P φ_(21) dx dy = (4/a^2) V_0 ∫_0^a ∫_0^a sin^2(πx/a) sin^2(2πy/a) dx dy = V_0 sin^2(π) sin^2(2) 0 dy The image contains a handwritten page filled with mathematical equations. The equations are primarily focused on calculating matrix elements (H_P11, H_P22, H_P12, and H_P21) involving double integrals of trigonometric functions. The calculations involve several steps, including integration and simplification. The overall layout is well-organized, with equations arranged in a clear structure. The handwriting is clear and legible. The image contains a handwritten page filled with mathematical equations. The equations involve various symbols and variables, including V, E, I, φ, T, π, m, ħ, α, R, and φ. There are matrices, quadratic equations, and expressions involving exponents and trigonometric functions. The overall layout is somewhat disorganized, with equations scattered across the page. The handwriting is generally legible, but some symbols and expressions are difficult to decipher due to image quality and inconsistent notation. The image contains a handwritten page filled with mathematical equations. The equations involve various symbols and numbers, including E, *, 10, 2, T, a, R, and 0. There are also seemingly random characters and words that do not appear to be related to mathematical expressions. The overall layout is disorganized, with equations and symbols scattered across the page. The handwriting is clear, but the content is difficult to understand due to the lack of context and the presence of non-mathematical elements.