Quantum Mechanics Answers

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.

Calculate the mean kinetic and potential energies of a simple harmonic oscillator
which is in its ground state.

) The wavefunction for a particle is defined by:
ψ (x)={ N cos(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. (5+5)

For the operator A = a x + i b p where a and b are constants, calculate [A, x] and
[A, A].

Use Heisenberg’s uncertainty principle to estimate the ground state energy of the
harmonic oscillator.

A body of mass 6kg is at rest when a force of magnitude 30 N on the body. After 10s what will be kinetic energy?

The wavefront for a particle is defined by:
Ψ(x)= {Ncos(2πx/L) for -L/4≤x≤L/4
{0 otherwise
How to determine:
i) the normalisation constant N,
ii) the probability that the particle will be found between x=0 and x=L/8.