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

2024
Views:

288

Pages:

7
Author:

Jabin F.

Particle exchange operator 8- An operator theet exchanges the particles in a pair, សំ Called particle exchange operator. The first line presents an equation involving curly brackets, parentheses, and the expression "{Pij}". The second line defines "Pij" as equal to "1" and the word "Mirror". There are no other visual elements or objects in the image. P_{ij} \psi(\vec{r}_i, \vec{s}_i; \vec{r}_j, \vec{s}_j) = \psi(\vec{r}_j, \vec{s}_j; \vec{r}_i, \vec{s}_i) ⇒ P_{ij}^2 \psi(\vec{r}_i, \vec{s}_i; \vec{r}_j, \vec{s}_j) = \psi(\vec{r}_i, \vec{s}_i; \vec{r}_j, \vec{s}_j) ⇒ P_{ij}^2 = \hat{I} mirror let ψ(ri,si; rj,sj) be the eigenfunction of Pij with eigenvalue λ. Pij ψ(ri,si; rj,sj) = λ ψ(rj,sj; ri,si) Pij² ψ(ri,si; rj,sj) = λ² ψ(ri,si; rj,sj) = ψ(ri,si; rj,sj) λ² = 1 ⇒ λ = ±1 The equations involve variables like 'Pij', 'izi', 'Bjj', 'ri', 'sc', 'Y', 'rosj', 'risi', and 'Miss'. There are also numerical values and operators like '+', '=', '(', ')', and ','. Below the equations, the phrase "Symmetric wave f" is centered. The equations involve variables like 'Pij', 'izi', 'Bjj', 'ri', 'sj', and 'risi'. There are also numerical values and operators like '+', '=', '(', ')', and ','. Below the equations, the phrase "Antisymmetric" is centered. ⇒ The particle exchange operator is Involuntary Pi = Î ⇒ The particle exchange operator is Hermitian, P = Pij ⇒ (Φ, PjY) = (PijΦ, Y) =) ⇒ The eigen value of particle exchange Operator are ±1. ⇒ The eigen in of particle exchange operater have definite symmetry. The eigen in Corresponding to the eigen value y symmetric. and Corresponds to -ve eigen value y antisymmetric. Pi 1346 ⇒ H= ++ √(ri, r₃) V [Pi,H]y (misijrjsj) = ( ) 4 (risi rjsj) [Pi,H3 = 0 if ve is symmetric Under the exchange of V(Tj) = √(ji) Particle in pair. [Pi,H]≠0 ⇒ it virirj) ≠ +v (rjiri) ⇒ Energy eigen fh. Corresponding to symmetric Poth have definite Symmetry. (for Non-interacting Particles) The content appears to be a physics or quantum mechanics problem with calculations and an answer. There are no discernible objects or people in the image. spin triplet 1↑↑> or 1117 7=2 \[E=\frac{\pi^{2}\hbar^{2}}{2mL^{2}}+\frac{4~\pi^{2}\hbar^{2}}{2mL^{2}}\] \[=\frac{(S)\Pi^{2}\hbar^{2}}{2~mi^{2}}\] (option-d) Probi Write the space of spin parts of enic have f" of He atom in goound state * First excited state. The content appears to be a solution or explanation related to the helium atom, possibly involving quantum mechanics concepts. There are mathematical equations, numbers, and labels such as "Soln Gis.", "Ground state", and "Singlet". No objects or people are visible in the image. The content appears to be a mathematical derivation or explanation related to the first excited states of a system, possibly in the context of quantum mechanics. There are equations, symbols, and labels, including "for first excited states", "Yopin Symmetric.", and "Yppin Antisymm.". No objects or people are visible in the image.