Frame of Reference - Edubirdie

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

2024
Views:

301

Pages:

5
Author:

Jabin F.

# Frame of Reference → Lab frame C.O.M. frame or L- frame C- frame offer The frame of Ref in → The frame of Ref. In which target initially Which com of the System is aluesyrat at Rest sest. 6 = Dof. (system) 63/Dot) → ineident particle, → 6Dof → 3Dof (relati motto, 3 (Dof) → target particle, #Dof of com = o Dof of system=(3+ 3)2 (comatrest) = Dof. (incidat + target) = Dof. (commotion + relativemotion) X_L = R + X_C d/dt X_L = d/dt (R + X_C) V-L = dR/dt + VC V_L = Vcm + VC Ques. 3 page-64 for central potential [L²,H]=0 → optim 3 में Cam होता है [H,Lz]=0 Ques. 5 page-63 14) = (11,-1)+11,0) exp(iπ/3) +11,1) exp(i2π/3) <ψ| = 1/√3 ((1,-1|+|1,0> exp(-iπ/3) + |1,+1> exp(-i2π/3)) S_m|ψ> = (S_+ + S_-)/2 |ψ> = 1/2 * 1/√3 (√2ħ|1,0> + e^(iπ/3) √2ħ|1,1> + ħ|0>) + e^(i2π/3) √2ħ|1,0>) <ψ|S_m> = <ψ|S_m|ψ> = 1/6 ( e^(i 2π/3) J ħ + e^(-i 2π/3) J ħ + e^(i π/3) J ħ + e^(-i π/3) J ħ ) = J 2ħ ( 2 cos 2π/3 + 2 cos π/3 ) / 6 = 4 J 2 ħ / 6 x 3 = J 2 ħ / 3 |z,+> = |↑>, (001) e^(-iσ_z π/4) e^(iπσ_y/4) |z,+> = ((σ_x/2 - iσ_z sin π/2) / √2 + (iσ_y sin π/2) / √2) |z,+> = (-iσ_z / √2 + (iσ_y / √2) |z,+> = -i/√2 (σz|z,+> + iσzσy|z,+>) = -i/√2 (|z,+> + i(iσx)|z,+>) = -i/√2 (|z,+> + |z,->) = -i/√2 (|1> + |1>) = -i/√2 [1] = |x,+> = (1,0,0) (option-b) Ques. 14 page-61 ρ = [I + 1/√3 (σx + σy + σz)] / 2 Tr(ρ) = 1/2 [Tr(I) + 1/√3 Tr(σx + σy + σz)] Tr(σx) = Tr(σy) = Tr(σz) = 0 = I = [0 1] [2x2] => Tr(I) = 2 Tr(ρ) = 1 Tr(ρ²) = 1 Tr(ρ²⁰¹⁷) = Tr(ρ¹⁶ ρ) Tr(ρ²⁰¹⁶ ρ) = 1 (option-c)

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