Exam Details
Subject | quantum mechanics and statistical mechanics | |
Paper | ||
Exam / Course | b.sc. physics (honours) | |
Department | ||
Organization | nalanda open university | |
Position | ||
Exam Date | 2016 | |
City, State | bihar, patna |
Question Paper
Nalanda Open University
Annual Examination 2016
B.Sc. Physics (Honours), Part-III
Paper-VI (Quantum Mechanics and Statistical Mechanics)
Time: 3.00 Hrs. Full Marks: 80
Answer any five questions. All questions carry equal marks.
1. What is hermitian operator? Show that two eign functions of Harmitian
operator, belonging to different eigen values are orthogonal to each other.
Explain the expectation value of a quantum mechanical operator.
2. Derive Schrodinger's equations in both time independent and time
dependent cases. What is the physical interpretation of wave function?
3. What is uncertainty principle? Derive Heisenberg's uncertainty relation for
the position and momentum variabels. Show that an electron connot exist
inside the nucleus.
4. Define angular momentum in quantum mechanics. Show that the
components of angular momentum commute with L2, whereas they do not
commute with each other.
5. A particle is incident on a one-demensional potential barrier of height V0
and width a. Deduce an expression for its transmission probability.
Discuss the two cases when the energy E of the particle is E>V0 and
V0.
6. What are symmetric and anti-symmetric wave functions? Discuss the
symmetry of a wave function, in detail.
7. State and prove Liouiville's theorem.
8. Establish the Fermi-Dirac distribution formula and hence obtain an
expression for Fermi energy.
9. Deduce Planck's rediation formula on the basis of Bose-Einstein's
statistics.
10. Find the relation between pressure and temperature of vapour treated as a
gas during liquid-vapour transition.
Annual Examination 2016
B.Sc. Physics (Honours), Part-III
Paper-VI (Quantum Mechanics and Statistical Mechanics)
Time: 3.00 Hrs. Full Marks: 80
Answer any five questions. All questions carry equal marks.
1. What is hermitian operator? Show that two eign functions of Harmitian
operator, belonging to different eigen values are orthogonal to each other.
Explain the expectation value of a quantum mechanical operator.
2. Derive Schrodinger's equations in both time independent and time
dependent cases. What is the physical interpretation of wave function?
3. What is uncertainty principle? Derive Heisenberg's uncertainty relation for
the position and momentum variabels. Show that an electron connot exist
inside the nucleus.
4. Define angular momentum in quantum mechanics. Show that the
components of angular momentum commute with L2, whereas they do not
commute with each other.
5. A particle is incident on a one-demensional potential barrier of height V0
and width a. Deduce an expression for its transmission probability.
Discuss the two cases when the energy E of the particle is E>V0 and
V0.
6. What are symmetric and anti-symmetric wave functions? Discuss the
symmetry of a wave function, in detail.
7. State and prove Liouiville's theorem.
8. Establish the Fermi-Dirac distribution formula and hence obtain an
expression for Fermi energy.
9. Deduce Planck's rediation formula on the basis of Bose-Einstein's
statistics.
10. Find the relation between pressure and temperature of vapour treated as a
gas during liquid-vapour transition.
Other Question Papers
Subjects
- classical electrodynamics, plasma physics, physics of atoms,molecules and nuclei
- classical mechanics and mathematical physics
- condensed matter physics & electronics
- electrostatics, magnetism current electricity and modern physics
- optics & electromagnetic theory
- physics
- quantum mechanics and statistical mechanics