Consider the three functions F(x₁, x₂) = =e₁ + x₂; 1 and 2 are particle labels. Which of the following statements are true? G(x₁, x₂) = x₂e1 + ₁e² and H = F (x₁, x2) - F(x2, x1) Both F and G are symmetric under interchange of particles G is symmetric under interchange of particles but not F OH is anti antisymmetric F is neither symmetric nor antisymmetric

find the values , (1) [§*, ê,] = izh ŷ (1) [x´, Px ] =izh ŷ 7. (2) [ P,P´]= o (3) [§, ê,' ] = 2ib ê J= 2ib p

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Imagine a laser medium behaves as a three-level system and the population inversion between states 2 and 3. The pump excites the atoms to the states 3 and 2 at a pump rate R3 and R2, respectively. State 3 decays back to 2 so slow. Use the lineshape function to find an expression of the small-signal gain coefficient.

Show 4100 and Þ 200 are orthogonal 3 1(Z \7 P100 3 1 V200 (2 – p)e 4/2n \ao. ||

Alpha particles of energy 8.4 MeV are incident on a silver foil of thickness 6.5 μm. For a certain value of theimpact parameter, the alpha particles lose exactly half their incident kinetic energy when they reach theirminimum separation from the nucleus. Find the minimum separation, the impact parameter, and the scatteringangle.

Show that at limit ħo kgT, the following expression, h €(w, T) = c exp(Bho)-1 reduces to the classical form given by: e(w, T)= Ac ³(kgT)w²: ² = 0 [₁²³ (²+²)]. Ac

A neutron is scattered through an angle of 60 degree in the C.M syste m in collision with Carbon.Find the fractional loss the energy of the neutrons.Also calculate the maximum fractional energy loss in this case?Use I given

Subject: physics

A lithium ion Lit++ (Z = 3, A = 6g/mol) with incident kinetic energy EK = 7.5MEV is scattered on a gold nucleus (Z = 79, A = 197g/mol) through an angle of 10°. Assume that the mass of the lithium ion is much smaller than the mass of the gold nucleus. Please answer the following questions: %3D (a) Calculate the impact parameter b; (b) Calculate the closest approach rmin-