PG model papers for physics

Approved in P.G.B.O.S. meeting held on 08-08-2008

Acharya Nagarjuna University M.Sc Physics I Semester
Model paper
PAPER- III : QUANTUM MECHANICS -I PHY 1.3

Answer the following Questions.
All Questions carry equal marks

Time : 3 hours Max. Marks 80

1 a). State and prove Ehrenfest’s theorem? Write the significance of the result.
b). Obtain the Eigenvalue of a particle in a finite Potential-well?

OR

c). Describe “Dirac” notations for state vectors, Eigen values, Orthogonality and
normalization, in quantum mechanics
d). Solve for eigen values and eigen functions of one Dimensional Harmonic oscillator by
operator method
2 a) Discuss the eigen value problem of L2 and Lz

OR

b) Discuss the eigen values and eigen functions of rigid rotator

3. a) Outline the time-independent Non-degenerate perturbation theory for obtaining the
energy levels of a stationary system and apply it to find the energy of the ground state of
Helium-atom

. OR

b) Derive the expressions for eigen values and eigen functions for a degenerate perturbation
system.
c) Explain linear Stark effect on hydrogen-atom?

4 . a) State and prove variation theorem.
b) Evaluate the ground state energy of helieum atom using varation method.

OR

c) Derive the expression for the transition probability using time dependent perturbation
theory.
d) Derive Fermi – Golden rule for the transition into continuum.

5 Write notes on any two of the following.
a) Hermitian-operator and it’s eigen values
b) Angular momentum in Quantum-mechanics
c) Adibatic approximation.
d) Einstein transition probabilities

MODEL PAPER
M.Sc.Physics ( I SEMESTER )
PAPER- IV : ELECTRONICS PHY 1.4

Time 3 hours Max Marks 80

Answer ALL Questions. All questions carry equal marks

1 a) Explain about the important electrical parameters of OP.AMP.
b) Explain the type of feedback used with amplifiers.

OR

c)With suitable diagrams explain how Op. Amp can be used to perform Summing, integration,
differentiation operations.

2. a) Draw the circuit diagram of a R-C phase shift oscillator and explain its working.
b) Give the reasons for instability in oscillator circuits.

OR

c) Draw the circuit diagram of adjustable IC regulated power supply and explain its working.
d) Explain the principle of working of switching regulator

3. a) Draw the circuit diagram to produce DSBSC modulation.
b) Explain the method of detecting DSBSC.

OR

c).What do you mean by decoder and encoder?
d) With truth tables explain the working of T-flip flop, D- flip flop JK flip flop and RS clocked
flip-flop.

4 a) Explain with functional block diagram the architecture of 8085.
b) Write an assembly language program to create time delay of 200 microseconds if the clock
frequency of 8085 processor is 1MHz.

OR

c) What do you mean by stack and subroutine?
d) Explain the architecture of microcontroller 8051.

5. Write notes on any TWO of the following
a) Differential amplifier and CMRR
b) Effect of negative feedback on gain and band width
c) Frequency division multiplexing
d) Memory organization

Approved in P.G.B.O.S. meeting held on 08-08-2008
Acharya Nagarjuna University M.Sc Physics II Semester
Model paper PHY 2.1
Paper 1 : Quantum Mechanics -II

Time: 3 hrs Max.Marks:80
Answer all questions

1. (a)What are C-G coefficients? Describe their properties
(b) Derive C-G coefficients for

(OR)

( c) Derive Pauli’s spin matrices
(d). Prove any three properties of Pauli’s spin matrices.

2. (a) What do you understand by a picture in quantum dynamics? What is the difference
between different pictures.
(b) Obtain the equation of motion in Heisenberg picture and explain constant of motion .

(OR)

(c) Establish the correspondence of quantum mechanical pictures with classical mechanics
with specific examples.
(d) Apply the Heisenberg picture to a harmonic oscillator and explain its significance.
3. (a) Discuss Born- approximation in scattering calculations.
(b) Calculate the differential cross-section for the square well potential.

(OR)

(c) Define the scattering cross-section according to classical mechanics and quantum theory.
(d) Discuss the significance of Green’s function in scattering theory.

4 (a) Explain L.C.A.O. Method.
(b) Solve the Schrödinger equation for the hydrogen molecule ion using L.C.A.O. Method.

(OR)

(c) Explain the essential principles of the Valence bond method and apply it for the problem of
hydrogen molecule.

5. Write notes on any TWO of the following .
(a) Wigner-Eckart theorem
(b) Creation and annihilation operators
(c) Optimal theorem
(d) Born –Openheimer approximation

MODEL PAPER
M.Sc.Physics II SEMESTER
PAPER- II. STATISTICAL MECHANICS PHY 2.2

Time :3hrs. Max.marks.80

Answer any five questions. All questions carry equal marks

1. a) State and prove equipartition theorem.
b) What is Gibb’s Paradox ? How was it resolved?

OR

c) Explain the concept of phase space and ensemble.Distinguish between three ensembles,
namely, Microcanonical, canonical and Grand canonical ensemble.
d) State and prove Liouvilles theorem .

2. a) Obtain expression for ensemble density in the canonical ensemble
b) Discuss energy fluctuations in canonical ensemble.

OR

c) Discuss the density fluctuations in the grand canonical ensemble and prove the equivalence
between canonical and Grand canonical ensembles.

3. a) Obtain the Sackur Tetrode equation for ideal Boltzmann gas on the basis of microcanonical
ensemble.

OR

b) Employing the method of Darwin and Fowler, derive the energy distribution for a canonical
ensemble.

4. a) Derive the equation of State of an ideal Fermi gas and discuss the Fermi energy and
pressure for ideal Fermi gas at low temperature and high densities.

OR

b). What is Bose -Einstein condensation? Explain the phenomenon using Grand partition
function. Explain the role of super fluidity and conductivity.

5. Write short notes on any TWO of the following
a) Entropy of classical ideal gas
b) Density matrix
c) Landau diamagnetism
d) Brownian motion

MODEL PAPER
SEMESTER-II
Paper- IV Solid State Physics (General) PHY 2.4

Time:3hrs. Max. marks.80

Answer ALL questions .All questions carry equal marks

1. a) What do you mean by periodic array of atoms ?
b) What do you mean by primitive lattice cell

OR

c) What are the various types of lattices?.
d)Describe the crystal structure of Diamond.

2.a) Derive Laue conditions for X-ray diffraction.
b) Compare the relative advantages and disadvantages of Laue’s powder and Rotating crystal
method of determining Crystal structures.

OR

c) Explain neutron diffraction method .
d) Explain why neutron diffraction is complementary to X-ray diffraction in the determination
of crystal structure.

3. a)What is free electron Fermi Gas
b)Obtain an equation for number of orbitals for unit energy in three dimensions.

OR

c) Explain the electrical conductivity process in a metal. Obtain an equation for electrical
conductivity
d) Discuss the quantization of orbits in magnetic field.

4.a) Describe the behaviour of the electrons in a periodic potential using Kronig-Penny model.
b) What are its important conclusions.

OR

c) Explain the crystal momentum of an electron
d) Describe the classification of band theory of solids.

5. Write short note on any TWO of the following.
a) Sodium chloride crystal structure
b) Reciprocal lattice to bcc lattice
c) De-Hass-van Alphen effect
d) Bloch theorem

Model paper
M.Sc Physics (III Semester)
Paper II: NUCLEAR AND PARTICLE PHYSICS PHY 3.1

Time: 3 hrs Max.Marks:80
Answer ALL questions All questions carry equal marks

1 a) Explain the features of binding energy per nucleon (B/A)versus mass number(A) curve
b)Obtain an expression for electric quadrupole moment of nucleus. What would be the value of
classical quadrupole moment for a single proton located at the nuclear equator?

OR

c) Obtain an expression for wave function for ground state of deuteron on the basis of central
force assumption
d) Describe the basic ideas in Yukawa’s meson exchange theory of the nuclear force and show
how the pion was postulated.

2. a) Explain how magic numbers are predicted based on the shell model of nucleus.
b) Determine the ground state spin and parity of the following nuclei 1) 6C13 2) 7N16 3)
28Ni61 4)33As75

OR

c)Explain the Gamow’s theory of alpha decay and hence derive the Geiger-Nuttal Law.
d) Explain the Mossbauer effect.

3. a) What is the Q-equation of nuclear reaction? How the nuclear reactions are classified based
on the Q- value?
b) Explain about the direct and compound nuclear reaction mechanisms. Give some examples.

OR

c) Explain the terms nuclear fission and nuclear fusion. Give some examples. discuss about the
energy release in nuclear fission.
d) Briefly describe various types of reactors.

4 a) How do you classify the electrostatic accelerators?
b) Explain the working principle of cyclotron.

OR

c) Explain the Rutherford back scattering
d) How nuclear medicine can be used for diagnostic purpose?

5. Write notes on any two of the following
a) Spin dependence of nuclear forces
b)Weizsacker’s semi empirical mass formula
c)Classification of elementary particles
d) SU(2) and SU (3) multiplet

Approved in P.G.B.O.S. meeting held on 08-08-2008
Acharya Nagarjuna University M.Sc Physics III Semester
Model paper
Paper 2:ADVANCED QUANTUM MECHANICS PHY 3.2

Time: 3 hrs Max.Marks:80

Answer the following questions. All questions carry equal marks

1 (a) Derive the Klein – Gordon relativistic wave equation for a free particle.
(b) What are the short comings of the Klein – Gordon equation? Explain how they are
removed by Dirac’s equation.

(OR)

(c) Develop Dirac’s relativistic theory of an electron.
(d) Show that the spin of electron is directly explained by Dirac’s theory .

2. (a) show that the Dirac equation is invariant under Lorentz transformations.
(b) Explain charge conjugation from Dirac’s theory.

(OR)

(c ) Obtain the free particle solutions (Dirac spinors) for a Dirac particle . Explain their
physical significance.
(d). Explain the Dirac equation for zero mass

3. (a) Explain the method of second quantization .

(b) Discuss the quantization procedure applied to Maxwell field

(OR)

(c) Discuss the difficulties of the relativistic unquantized Dirac equation
(d) Discuss the quantization of Dirac field.

4. (a) Give the Classical field theory of Real scalar field and obtain for the Lagrangian.

(b) Explain the quantization of real scalar field .

(OR)

(c) Write down the Hamiltonian for an atom in the presence of radiation field. Solve the Wave
equation to obtain the formula for transition probability.
(d) Discuss the transition probabilities for emission and absorption in radiation field.
5. Write any TWO of The Following :
(a) Dirac matrices and their properties.
(b) Negative energy solutions.
(c) Creation, annihilation and number operators and their physical significance.
(d) Hamiltonian formulation of a classical field.

Approved in P.G.B.O.S.meeting held on 08-08-2008
Acharya Nagarjuna University M.Sc Physics IV Semester
Model paper PHY 4.1
Paper I:ELECTROMAGNETIC THEORY AND MODERN OPTICS

Time: 3 hrs Max.Marks:80
Answer all questions

1. a) State the boundary conditions that are to be satisfied by the electric and magnetic fields at
the surface of separation of two dielectric media.
b) Deduce the expressions for the intensity of the reflected and transmitted wave is incident
at such an interface.

OR

c) What is double refraction and discuss the propagation of light in double refracting media.

2. .a) Explain the working of ruby laser .
b) Discuss the line broadening mechanism.

OR

c) What are the central features of semi conductor lasers.
d) Derive the expression for the laser action in semiconductor laser.

3. a) Give the basic principles of holography and explain its importance and uses.

OR

b) Write in detail about Fourier transform holography

4 a) Discuss in detail the mode theory of circular wave guides.
b) Discuss various types of dispersions in optical fibers.

OR

c) Explain the structure and advantages of a step index optical fiber
d) Explain the signal degradation in optical fibers.

5 Write notes on any two of the following
a) Retarded Potentials
b) Population Inversion
c) Speckle pattern
d) Attenuation in optical fibers