Calculate the Born approximation to the differential and total cross actions for scattering a particle of mass m off the d-function potential V(r) = g8"(r).
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![Calculate the Born approximation to the differential and total cross
ctions for scattering a particle of mass m off the d-function potential
V (r) = g8*(r).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F708e8fb9-c67f-402d-8543-0484e6f007d2%2F11748cea-d083-4316-a6e5-08c14e50a9c9%2Fys9l3pa_processed.jpeg&w=3840&q=75)
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- Expand the equation K = m(γ−1) in aTaylor series, and find the first two nonvanishingterms. Explain why the vanishing terms are theones that should vanish physically. Show thatthe first term is the nonrelativistic expression forkinetic energy.Consider a uniform source of neutrons in a diffusive, non-absorbing medium located between two concentric spheres of radii a and b > a. The inner part of the sphere of radius a contains a perfectly absorbing material; the outer surface of the sphere of radius b is a perfect mirror (albedo equal to one). Derive an expression for the flux between a and b.6QM Please answer question throughly and detailed.
- A neutron of mass m of energy E a,V(x) = Vo ) II. Estimate the kinetic energy of the neutron when they reach region III.Consider the one-dimensional step-potential V (x) = {0 , x < 0; V0 , x > 0}(a) Calculate the probability R that an incoming particle propagating from the x < 0 region to the right will reflect from the step.(b) Calculate the probability T that the particle will be transmitted across the step.(c) Discuss the dependence of R and T on the energy E of the particle, and show that always R+T = 1.[Hints: Use the expression J = (-i*hbar / 2m)*(ψ*(x)ψ′(x) − ψ*'(x)ψ(x)) for the particle current to define current carried by the incoming wave Ji, reflected wave Jr, and transmitted wave Jt across the step.For a simple plane wave ψ(x) = eikx, the current J = hbar*k/m = p/m = v equals the classical particle velocity v. The reflection probability is R = |Jr/Ji|, and the transmission probability is T = |Jt/Ji|. You need to write and solve the Schrodinger equation in regions x < 0 and x > 0 separately, and connect the solutions via boundary conditions at x = 0 (ψ(x) and ψ′(x) must be…(d) Prove that for a classical particle moving from left to right in a box with constant speed v, the average position = (1/T) ff x(t) dt = L/2, where T L/v is the time taken to move from left to right. And = : (1/T) S²x² (t) dt L²/3. Hint: Only consider a particle moving from left x = 0 to right x = L = and do not include the bouncing motion from right to left. The results for left to right are independent of the sense of motion and therefore the same results apply to all the bounces, so that we can prove it for just one sense of motion. Thus, the classical result is obtained from the Quantum solution when n >> 1. That is, for large energies compared to the minimum energy of the wave-particle system. This is usually referred to as the Classical Limit for Large Quantum Numbers.