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

2024
Views:

73

Pages:

5
Author:

Jabin F.

Equations or expressions related to a variable 'y' and its components. The symbols 'Sy', 'y', and 'lambda' are likely representing specific quantities or operations within the context of a larger mathematical problem. The presence of inequalities ('>') suggests that the equations might be part of a system of equations or inequalities involving constraints or conditions. The numerical values and fractions indicate calculations or comparisons. The equations involve variables y, a, and potentially others represented by symbols. There are also numerical values, operators, and symbols such as parentheses, brackets, and inequality signs. The equations are arranged vertically, with some horizontal alignment. The handwriting is clear, although some symbols might be ambiguous due to the handwriting style. Prob. A spin particle is in the spin State |1/4> = [ ] (i) If spin of the particle is measured, what are the probabilities of finding its spin along z-direction & with possible result of measurement. 1 (ii) Find the expectation value of Sz (iii) If spin of the particle is measured, What are the probabilities of finding its spin along x-direction and possible outcome 1 • of measurement. (iv) Find the expectation value of Su Sol (i) [|\Psi>=\frac{i}{\sqrt{6}}(\begin{matrix}i+i\ 2\end{matrix})] ! = C₁ |1> + C₂ |2> = C₁ |+> + C₂ |-> \[C₁=<ψ(+)|\psi>=(\begin{matrix}0&1\end{matrix})\frac{1}{\sqrt{6}}(\begin{matrix}i+i\\ 2\end{matrix})=\frac{2}{\sqrt{6}}\] \[C₂=<ψ(-)|\psi>=(\begin{matrix}1&0\end{matrix})\frac{1}{\sqrt{6}}(\ [P_{2}^{(\underline{ve}}{|c_{2}|}^{2}=\frac{4}{6}=\frac{2}{3}] (|\frac{1+i}{\sqrt{6}}|^{2}=1-\frac{2}{3}=\frac{i}{3}) Fald 介 The possible result of measurment. (\pm\frac{\hbar}{\alpha^{9}}) for (\frac{-\hbar}{2}) , [P_{2}=\frac{2}{3}] [+\frac{\hbar}{2}\rightarrow P_{i}=\frac{1}{3}] (ii) (=_{:}\frac{\langle\Psi|S_{z}|\Psi\rangle}{\langle\Psi|\psi\rangle}) = <257 (iii) (|\psi>=\frac{1}{\sqrt{6}}(\begin{matrix}i+\tilde{i}\ 2\end{matrix})=&c_{1}|\psi_{n}(+)>+c_{2}|\psi_{n}(-)>) \[=\frac{i}{\sqrt{112}}(it\dot{i}+2)=\frac{3+\dot{i}}{\sqrt{|2}}\] \[\mathcal{C}_{1}=\langle\psi_{\eta}(t)|\psi\rangle=\frac{1}{\sqrt{2}}(11)\frac{1}{\sqrt{6}}(\begin{matrix}1+\tilde{i}\\ 2\end{matrix})\] \[C_{2}=\langle\psi_{(\lambda}(-)|\psi\rangle=\frac{1}{\sqrt{2}}(i-i)\fr The content seems to be related to probability or statistics, with calculations involving fractions and possibly variables like P and C. 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.