A particle of mass m is free to move in one dimension. Denote its position coordinate by X and its momentum by p. Suppose that this particle is confined within a box so as to be located between a energy is known to lic between E and E+ SE. Draw the classical phase space 0 and x = L, and suppuse that its

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…

Operators in Quantum Mechanic (a) Give the definition of the term "Operator" ? (b) Name the Momentum Operator (c) Name the Total Energy Operator (d) Name the Hamilton Operator 3

In the pair production process, photon energy gets converted to particle/antiparticle pairs. Imagine a single photon in free space, turning into one electron and one positron (antielectron), each with mass mec?. Assume for simplicity both particles move together with equal momenta in the same direction as the original photon as shown, and the photon disappears. Prove this can't happen!

A particle with the velocity v and the probability current density J is incident from the left on a potential step of height Uo, that is, U (x) = Uo at r > 0 and U(x) = 0 at r 0.