What does population vector, Π=(P1,P2,P3r,P3w)T mean ? How do this formula describe the overall state probability? (there are state 1, state 2 and state 3w, 3r)

Need help with the following statistical thermodynamics problem!

What is the energy level difference between adjacent levels ∆En = En +1 - En for the simple harmonic oscillator? What are ∆E0, ∆E2, and ∆E20? How many possible energy levels are there?

We can finally calculate the uncertainty in the axial distance using the relation where o, is the uncertainty in r. Find the uncertainty in the axial distance of the particle's location.

An electron with an initial kinetic energy of 1.542 eV (in a region with 1.095 eV potential energy) is incident on a potential step (extending from x=0 to ∞) to V=2.381 eV. What is the transmission probability (in %)? FYI: If we had a travelling wave arriving at a similar potential DROP, then k1 (for x<0) would be real and the symmetry of R=(k1-k2)2/(k1+k2)2 implies reflection/transmission are the same as a potential RISE with the same energies but k1 and k2 swapped.

For a particle in a one-dimensional box, - calculate the probability of finding a particle in the second and third quarters of the box.      - What is this quantity for the fourth quarter?

Answer in 90 minutes please. Count as double the questions if necessary.

A dart hits the small square target shown below at a random point. Find the probability that the dart lands in the shaded circular region. Each side of the target is 15cm, and the radius of the shaded region is 5cm?

At zero temperature, Nb3Sn has the critical fields Bel = = 26 mT and B2 = 29 T. Determine the coherence length (§), penetration depth (X), Ginzburg-Landau parameter (k), and thermodynamic critical field (B₂).

For T = 0.3 sec, write the element of the discrete sequence corresponding to the function f(t) = 5t with k = 18. Provide your answer in seconds to the nearest first decimal place. Pay attention to the numbers given