Test Discussion - Edubirdie

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

2024
Views:

485

Pages:

7
Author:

Jabin F.

Test Discussion (Test-I) Soln E, θ = 90° E' = hc/λ' λ' = λ + Δλ Soln λ' = hc/E + h/moc(1-cos90°) Voco E' = hc/λ' = hcEmoc/h(moc^2+E) E' = E+moc^2 (option-d) Soln 2 fer e- v1 = 0.6c (Relativistically) v2 = 0.8c λ1/λ2 = h/p1 / h/p2 = p2/p1 = mov2/√(1-v2^2/c^2) / mov1/√(1-v1^2/c^2) = (v2/v1) * √((1-v1^2/c^2)/(1-v2^2/c^2)) = 0.8/0.6 * √((1-0.6^2)/(1-0.8^2)) = 4/3 = (+) (option-c) Sol3-8 T^L f(n) = f(n-L) [T^L, x^L] ψ(n) = (T^L x^L - x^L T^L) ψ(n) = T^L x^L ψ(n) - x^L T^L ψ(n) = (x-L)^L ψ(n) - L x^(L-1) ψ(n-L) = x^L ψ(n) - L x^(L-1) ψ(n-L) - L x^(L-1) ψ(n-L) + L^2 x^(L-2) ψ(n-2L) = - L^2 ψ(n-L) [T^L, x^L] ψ(n) = - L^2 ψ(n-L) => [T^L, x^L] = - L T^L (option-b) Sol2-4 Linear Cond'n A(c1 φ1(n) + c2 φ2(n)) = c1 A φ1(n) + c2 A φ2(n) option-a A ψ(n) = ψ(n) + 3 A(c1 φ1(n) + c2 φ2(n)) = c1 φ1(n) + c2 φ2(n) + 3 R.H.S -> c1 A φ1(n) + c2 A φ2(n) = c1 (φ1(n) + 3) + c2 (φ2(n) + 3) = c1 φ1(n) + c2 φ2(n) + 3(c1 + c2) L.H.S. Sol2-6 [\psi(m) = \sum_{n=0}^{\infty} (\frac{i}{\sqrt{3}})^n \phi_n(m) ] [= \phi_0(m) + (\frac{i}{\sqrt{3}})\phi_1(m) + (\frac{i}{\sqrt{3}})^2\phi_2(m) + \cdots ] for third state m = 2 The probability of Third state [P_2 = \frac{|C_2|^2}{\sum_{m}|C_m|^2} = \frac{|(\frac{1}{\sqrt{3}})|^2}{1 + |\frac{1}{\sqrt{3}}|^2 + |(\frac{1}{\sqrt{3}})^2| + \cdots} ] [= \frac{(\frac{1}{3})^2}{\sum(1-\frac{1}{3})} = \frac{\frac{1}{9}}{\sqrt{(\frac{2}{3})}} ] Sol2-7 m = 1 ψ(m) = ψ_0 e^{\frac{-\lambda m^2}{4}} ħ = 1, V(m) = ? 2 Ηψ(m) = Εψ(m) (10)ch (20) = Εψ(m) [(\frac{-\hbar^2}{2m} \frac{d^2}{dm^2} + V(m)) \psi(m) = E \psi(m) ]

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