M.Sc.(Semester II) (CBCS) Examination Oct/Nov-2017
Physics (Materials Science)
QUANTUM MECHANICS
Day Date: Friday, 17-11-2017 Max. Marks: 70
Time: 10:30 AM to 01.00 PM
Instructions: 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
Which one of the following objects, moving at the same speed, has the
greatest de Broglie Wavelength?
Neutron Electron
Tennis ball Alpha particle
Knowledge of the wave function of a particle enables the probabilities
of the particle's position, momentum, energy and other characteristic
to be calculated. In classical physics, what is the analogue of the wave
function?
The particle's momentum
The particle's energy
The particle's size
The sum of the forces on the particle
The wave function for a particle must be normalizable
The particle's charge must be conserved
The particle's momentum must be conserved
The particle cannot be in two places at the same time
The particle must be somewhere
Quantum tunneling occurs in
Nuclear fusion
Radioactive decay by emission of alpha particles
The scanning tunneling microscope
All of the above
The hydrogen atom is in d-state. For this state, the value of more


The travelling harmonic waves which have a constant magnitude at
great distances and for which the normalization integral diverges
represent
Free particles Restrained waves
Localized waves All of the above
Page 2 of 2
SLR-MO-518
State True or False: 08
The electromagnetic radiation has both the particle and wave nature.
The wave function and its first derivative with respect to its variables
are continuous.
The zero-point energy of an electron in a box is given by
Ezero point

8me a2
A transition between a pair of states is possible if the sum of or
difference in quantum numbers is an odd number.
The wave functions for different states of a harmonic oscillator are
mutually orthogonal.
If be the trial wave function of a system whose Hamiltonian H has a
discrete Eigen spectrum, then H E0.
For many electron atoms, the electron repulsion terms must be
excluded in the potential energy term of the wave equation.
The Born-oppenheimer approximation breaks down if there is
degeneracy among the energy levels.
Q.2 Write short notes on: 14
Interpretation and properties of the wave function ψ. 05
Shape of atomic orbital's. 05
The Hamiltonian of many-electron systems 04
Q.3 Obtain the equations for the transformations of the operators z L ˆ x L ˆ y L ˆ
and 2 ˆL from three dimensional rectangular coordinates to spherical polar

10
Show that the product of two hermitian operators is hermitian if they
commute.
04
Q.4 Consider a symmetric "1-D rigid box" of length




0
V


Obtain the energy Eigen values and Eigen functions.
08
Normalize the energy Eigen functions for a particle in a symmetric 1-D
finite box (only even parity).
06
Q.5 Discuss in detail the vibration and vibration spectra of diatomic molecules. 08
Show that the magnetic moment vectors which have the different
orientations with respect to the external magnetic field have different
energies determined by the quantum number M.
06
Q.6 Show that how the Hartree and Hartree-Fock self consistent field methods
are powerful methods for obtaining the ground state energy and wave
functions of many-electron atoms.
10
Write down the 1s orbital of the hydrogen atom obtain the probability
density ψ15 2
04
Q.7 Explain the Fourth postulate of quantum mechanics. 08
Prove that, if two operators and commute then they have the same
set of Eigen functions.