P= D„Ðx= (-in- Assume that -in- dx dx dx2 Evaluate < p?> for a particle in a box with 0 =m?v² h?n? II

What is the correct solution for this questions ? *Quantum physical chemistry *

4) Consider a particle in a 1D box in its ground state such that Þ(x) = Bsin where Bis a constant and Lis the length of the box i) P1 Calculate P2 Where P, is the probability of finding the particle inside a small "volume" element dx atposition x = L/2, and P2 is the probability of finding the particle inside a small "volume" element dx at position x = L/20 ii) Briefly discuss the significance of your result for part i).

1 Find the eigenvalues and eigenstates of the spin operator S; of an electron in the direction of a unit vector n; assume that n; lies in the yz plane. Find the probability of measuring S, = -

G.265.

Consider an isotropic three-dimensional harmonic oscillator for a particle of mass  "m" and the Hamiltonian  H=P2/2m + m(w0)2R/2 Where P and R are the three-dimensional momentum and position operators w0 angular frequency. Find the eigenvalues and the eigenfunctions of the Hamiltonian and the degrees of degeneracy for the energy levels.

please answer part c in details

4

The largest known element, francium, has an atomic diameter of 540 pm. What is the minimum uncertainty in the momentum of a a francium electron if the uncertainty in its position is taken to be the diamter of the atom? (pico = 10-12)

Identify the normalized wavefunction for a particle rotating about the surface of a sphere with a fixed radius with I= 1 and mj = ±1. 1 3 e tiø Psine 2 V 2 1 y =, 土ゆ 2 T 3 sine e tip 2