M.Sc. (Semester II) (CBCS) Examination Nov/Dec-2018
Physics (Materials Science)
QUANTUM MECHANICS
Time: 2½ Hours Max. Marks: 70
Instructions: Q 1 and Q 2 are compulsory.
Attempt any three questions from Q. 3 to 7.
All questions carry equal marks.
Q.1 Choose correct alternatives. 08
Expectation value for position is not given by
Which one is not a condition that the wave functions must meet in
order to be acceptable.
must exist and satisfy the Schrödinger equation.
and dψ/dx must be continuous, finite and single valued.
fast enough as so that the normalization intergral
remains bounded.
None of the above
An electron is in an infinite square well that is 9.6 nm wide. The electron
makes the transition from the n=14 to the n=11 state. The wavelength of
the emitted photon is closet to:
3400 nm 4100 nm
2800 nm 4700 nm
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 sinusoidally with thickness
It decreases linearly with thickness
It decreases exponentially with thickness
Particles with half integral spin obey
Fermi-Bose Statistics Bose- Einstein Statistics
Fermi-Dirac Statistics Dirac- Einstein Statistics
Which of the following statement is true?
Exchange interactions are purely classical-mechanical interactions,
acting even on distant electrons.
Exchange interactions are purely quantum-mechanical interactions,
acting even on distant electrons.
Exchange interactions are purely quantum- mechanical interactions,
acting on nearby electrons only.
Exchange interactions are purely classical-mechanical interactions,
acting on nearby electrons only.
The approximation neglecting atomic nuclear motions to consider
electronic motions is called the adiabatic approximation is also known

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SLR-VN-381
Fermi approximation
Born-Oppenheimer approximation
Dirac approximation
None of the above
In simple harmonic oscillator, energy levels have spacing.
Increasing Unequal
Decreasing Equal
State True or False 06
Energy of Harmonic Oscillator becomes zero at zero degree Kelvin.
An electron moving in a thin metal wire is a reasonable approximation of
a particle in a one dimensional infinite well.
Probability density can be dependent on time.
Spin of the particle is a non-relativistic effect.
There is a Hartree-Fock equation for each electron in the molecule.
LCAO stands for linear combination of atomic orbitals.
Q.2 Write a short answers:
Prove that the eigenfunction of a Hermitian operator corresponding to different
eigenvalues will be orthogonal functions.
05
Define linear operator. Why linear operators are relevant in Quantum
Mechanics.
05
Write the postulates of operator formalism of Quantum Mechanics. 04
Q.3 Show that ground state wavefunction of 1-D simple harmonic oscillator
Find and for the second excited state in an infinite
square well potential.
06
Q.4 Give a detailed description of Hartree Fock self consistent field methods. 08
Given the functions f (x1
2 and show that, for x1
is unsymmetric for exchange of the two x positions, f
is symmetric, and f is antisymmetric.
06
Q.5 The energy needed to detach the electron from a hydrogen atom is 13.6 eV,
but the energy needed to detach an electron from hydrogen molecule is 15.7
eV. Why do you think the latter energy is greater? The protons in the H2

molecular ion are 0.106 nm apart and the binding energy of H2
is 2.65 eV.
What negative charge must be placed halfway between two protons this
distance apart to give the same binding energy?
08
What are the postulates of molecular orbital theory? 06
Q.6 Consider two electronic states, nearly degenerate, having parallel potential
energy curves. Let Q be the nuclear coordinates the induces coupling
between these two states. Show that, as a consequence of Born-
Oppenheimer breakdown, after the coupling of these two states due to the
nuclear motion the lower energy state has the symmetrically disposed
double minima in the potential energy curve along this mode Q.
08
Whether wave function must be antisymmetric for exchange of electron space
and spin coordinates? Argue by taking example.
06
Q.7 By mentioning the expression of normalized hydrogen atom wave function,
discuss its spatial nature.
08
Can a molecule have zero vibrational energy? Zero rotational energy?
Explain.