Quantum Mechanics Answers

Consider a particle in a Coulomb potential in three dimensional space. In Heisenberg's picture,d/dt⟨L^z⟩=0, where L^z is the z-component of angular momentum operator. Using this information which of the following choice(s) are correct:
1.H,L^z,L^x share simulatenous eigenbasis

2.L^z,L^x share simultaneous eigenbasis

3.H,L^z share simultaneous eigenbasis

4.L^.L^,L^z,L^x share simultaneous eigenbasis

The wavefunction for a particle is defined by:
ψ(X)= [NCos(2πx/L, for –L/4≤x≤L/4
[ 0, otherwise
Determine
i) the normalization constant N, and
ii) the probability that the particle will be found between x = 0 and x = L / 8.

Three Identical spin-half fermions are to be distributed in two non-degenerate distinct energy levels. The number of ways this can be done is.
1)8
2)4
3)3
4)4

What should the nature of the wave function be used to represent an electron in a crystalline solid?

When an object of mass 200g is submerged in methanol, its apparent weight is 1.052N. When submerged in benzene, its apparent weight is 0.951N. if the density of methanol is 0.8g/cm3, what is the density of benzene?

The massless spring of a spring gun has a force constant k = 0.04 N/cm. When the gun is aimed vertically, a 30 g projectile is shot to a height of 5.0 m above the end of the expanded spring. How much was the spring compressed initially? (Find d, in meters.)

A thermal neutron with a speed v corresponding to the average thermal energy at temperature T=300K is incident on a crystal. Will a diffraction pattrrn be obtained? Explain.

A minimum force 5N is required to make a body of mass 2kg move on a horizontal floor.
But a force 4N is required to maintain its motion with a uniform velocity. Calculate
coefficient of static friction and coefficient of kinetic friction.

Obtain the most probable value and expectation value of r for the ground state of a
hydrogen atom.

For a motion of a particle of mass μ in a spherically symmetric potential show that
L2 and Lz commute with the Hamiltonian.