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In the Large Electron Positron collider at CERN (an experiment which ended in the year 2000), groups
of electron and positrons were accelerated along a circular tunnel, so that they collided.
Electromagnets were used to keep the particles moving in a circle. Discuss how the strength and
direction of the magnetic field would need to be adjusted to:
i) keep a particle travelling in a circle while it is increasing its speed
ii) bend the paths of both positrons and electrons which are travelling in opposite directions in the same tunnel
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.
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

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.
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