M.Sc.(Semester II) (CBCS) Examination, 2017
PHYSICS (MATERIAL SCIENCE)
Quantum Mechanics
Day Date: Wednesday, 19-04-2017 Max. Marks: 70
Time: 10:30 AM to 01.00 PM
N.B. Q. No. and Q. No are compulsory.
Attempt any three from Q. No. to Q. No.
Use of Non programmable calculator is allowed.
All questions carry equal marks.
Q.1 Choose correct alternative: 06
How does the probability of an electron tunneling through a
potential barrier vary with the thickness of the barrier?
It decreases inversely with thickness.
It decreases sinusoidely with thickness.
It decreases exponentially with thickness.
It decreases linearly with thickness.
2 Which of the following is an accurate statement concerning
the simple harmonic oscillator?
The potential energy varies linearly with displacement
from equilibrium.
The spacing between energy levels increases with
increasing energy.
The wave functions are sinusoidal functions.
The number of nodes of the wave function increases with
increasing energy.
3 The ground state energy of a harmonic oscillator is



4 Partices in degenerate energy levels all have the samea)
Momentum Quantum numbers
Energy All the above
5 When the potential energy of a system is independent of time,
the wave function of the system
Cannot be normalized
Is directly proportional to the time
Depends on the vector positions, of each particle in the
system.
Is constant
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6 If the interaction of a particles with its environment restricts the
particle to a finite region of space, the result is the
quantization of of the particle.
The momentum The energy
The velocity All the above properties
State True or False: 08
The integration of probability density, over all space
must be unity.
To every physically measurable quantity of a system there
corresponds an operator in quantum mechanics.
The eigen values of an unitary operator have modulus zero.
A transition between a pair of states is strictly forbidden, if the
sum of or difference in quantum numbers is an even number.
The type of orbitals are spherical and have infinite density
on the nucleus.
The spin-orbit coupling splits the multiplet states of atoms and
is responsible for the fine- structure in atomic spectra.
If be the atomic orbitals on atoms ….n
respectivety, then molecular orbitals are approximately written
as Σ
.
The small splitting of the energy levels suggests that the
electron does not possesses an intrinsic magnetic moment.
Q.2 Write short notes on: 14
Wave and particle nature of radiation 05
Characteristic of the wave functions 04
For a simple potential barrier, show that the intensities of the
reflected and the incident beam are in the ratio equal to one.
05
Q.3 A particle moves in a one dimensional rigid box segment of length
and is in its ground state. If the right extremity of
the box suddenly expands to then what is the probability
that
The particle still retails its energy?
ii) Loses energy? gains energy?
10
Prove that the linear momentum operator is hermitian. 04
Q.4 Obtain the total wave function of a rigid rotator in the form
08
Calculate the few spherical harmonics as
ii)
06
Q.5 For a system of many electronics, obtain the overcall wave
function of a n-electron system. Write the overall wave function in
a determinant form.
10
For the Helium atom, write the Hamiltonian operator and the
overall wave function. Then obtain the energy which is always
higher than true energy, of the ground state.
04
Q.6 What is the Born-Oppenheimer approximation? Write the
complete wave equation for it. Interprot each term of the wave
equation.
08
How the linear combination of atomic orbitals (LCAO) stands the
basis for the calculation of approximate energies and molecular
orbitals in molecules? Explain.
06
Q.7 Discuss the probability densities for the is hydrogen atomic
orbitals.
06
How the shapes of atomic orbitals are determined? Explain in
detail.