BABSc, B.Com & BCA Questions _III - Nalanda Open University

Nalanda Open University
Annual Exam-2010,
Bachelor of Science (Physics) Hons, Part-III
(Quantum Mechanics & Statistical Mechanics)
Paper-VI
Time: 3 Hrs Full Marks: 75
Answer any FIVE questions. All questions are of equal marks.
1. (a) Show that two eigen functions of Hermitian operators, belonging to different
eigenvalues are orthogonal.
(b) A ball of mass 10 gm. has velocity 100 cm/sec. Calculate the wavelength
associated with it. Why does not this wave nature show up in our daily
observations?
(Given h= 6.62 × 10 -34 Joule.Sec)
2. Derive time dependent SchrÖdinger equation for the motion of a non-relativistic
material particle.
3. A particle of mass m and total energy E moves from a region of zero potential ( v
(x) = 0 When x < 0 ) to a region of constant potential
( v
(x) = V 0 When x > 0 ). Derive expressions for the reflection and transmission
coefficients.
4. A particle of mass m moving freely along the x-axis between two rigid walls
situated at x = 0 and x = L. Determine the allowed values of energy and the
corresponding normalised wave functions.
5. Define angular momentum. Show that the components of angular momentum do
not commute.
6. Write the possible states of the He- atom and write down its Hamiltonian. Hence
find the ground state of He- atom and its energy.
7. State and prove Liouville's theorem.
8. Apply grand canonical ensemble theory to obtain free energy and internal energy of
a perfect gas.
9. Find the relation between pressure and temperature of vapour treated as a gas
during liquid-vapour transition.
10. Establish the Fermi-Dirac distribution formula and hence obtain an expression for
Fermi energy.
κ κ κ