State Born-Oppenheimer’s approximation and its significance.
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Using the variational method, approximate the ground-state energy of a particle in a one-dimensional box with the trial wavefunction . Normalize the wavefunction and calculate the expectation value of energy.
Provide the transformation matrix for a rotation.
Derive the expression for the rotational energy levels of a rigid rotor.
Define a blackbody and discuss why classical mechanics failed to explain the blackbody radiation problem.
Calculate the energy of the first excited state of an electron confined to a one-dimensional box with . (3 + 2 = 5 marks)
(b) Define degeneracy and calculate the degeneracies of the first five energy levels for a particle of mass confined to a cubic box of edge length
.
Formulate the Schrödinger wave equation for the hydrogen atom and outline the stages involved in solving it.
Justify the statement: "The average distance of the electron in the ground state of hydrogen atom is more than its most probable distance in the same state."