ANDHRA UNIVERSITY
DEPARTMENT OF NUCLEAR PHYSICS
PROPOSED CORE, ELECTIVE AND SPECIAL COURSES TO BE OFFERED UNDER
M.Sc. (NUCLEAR PHYSICS) PROGRAMME AFFECTIVE FROM 2004 – 06 ADMITTED BATCH
Semester I Name of the Paper Max. Marks
Paper 1 1.1 Mathematical methods of Physics 100
Paper 2 1.2 Classical Mechanics and Special Theory of Relativity 100
Paper 3 1.3 Quantum Mechanics I 100
Paper 4 1.4 Electronic Devices and circuits 100
Lab Course: 1.5 Practical 200
Semester II
Paper 1 2.1 Atomic and Molecular Physics 100
Paper 2 2.2 Quantum Mechanics II 100
Paper 3 2.3 Electrodynamics 100
Paper 4 2.4 Statistical Mechanics 100
Paper -5 2.5 Non – Core Paper : Introductory Nuclear and Neutron Physics 100
Lab Course: 2.6 Practical 200
Semester III
Paper 1 (Special) 3.1 Nuclear Spectroscopy 100
Paper 2 3.2 Nuclear and Particle Physics 100
Paper 3 (Special) 3.3 Nuclear Radiation Detectors, Data Acquisition and Analysis 100
Paper 4 3.4 Computational Methods and Programming 100
Paper 5 3.5 Non – Core Paper : Experimental technique and Applied
Nuclear Physics 100
Lab Course: 3.6 Practical 200
Semester IV
Paper 1 (Special) 4.1 Nuclear Reactions and Particle Accelerators 100
Paper 2 (Elective) 4.2 Reactor Physics 100
Paper 3 4.3 Condensed matter Physics 100
Paper 4 (Special) 4.4 Nuclear Techniques in material Science and Radiation Physics 100
Lab Course: 4.5 Project Work 150
Viva – Voce 4.6 Comprehensive Viva – Voce 50
SEMESTER – I PAPER – 1
MATHEMATICAL METHODS OF PHYSICS
MODULE - I
1. Special Functions: (Without Power Series Solutions)
Beta and Gamma Functions: Definition and Simple Properties
Bessel Functions of The first kind: Generating Function, Recurrence Relations, Differential Equation
satisfied by Bessel functions, and Integral representation.
Hermite, Laguerre And Legendre Polynomials : Generating Functions, Recurrence Relations, Rodrigue's Formulae, Orthogonality and Normalisation properties , and Differential Equations satisfied by these Polynomials, Associated Legendre Polynomials and Spherical Harmonics
Text Book Reference Book: Mathematical Methods for Physicists G. Arfken : Ch 10. sec10.1,.4; Ch 11 sec11.1;
Ch 12 Sec12.1,.2,.3,.5,.6; Ch 13 sec13.1,.2
2. Laplace Transforms: Definition and Simple properties of Laplace Transforms, Laplace transforms of
Elementary functions, Laplace transforms of Derivatives, Inverse Laplace Transform, Applications of
Laplace Transforms
Text and Reference Book: Mathematical Methods for Phyisicists by G. Arfken
Ch 15 Sec 1,7,8, 9,11,
MODULE - II
3. Functions of Complex Variable:
Analytic Functions, Cauchy-Riemann Conditions, Cauchy's Fundamental theorem, Cauchy's Integral
Formula, Taylor's series, Laurent's series, Singularities, Classification of Singularities, Cauchy's Residue
Theorem, Application of Residue Theorem to evaluate simple Contour Integrals.
Text and Reference Book : Functions of Complex Variable with applications E. G. Phillips
Ch 1 sec5,6,7; Ch 4 sec30 to 36; Ch 5 Sec 43 to 46
4. Tensor Analysis:
Concepts of Tensor, Contravarient, Covaririent and Mixed Tensors, Addition and Subtraction of Tensors,
Contraction of a Tensor, Outer product and inner product of two tensors, Quotient law,
Text and Reference Book: Tensor Calculus by Barry Spain
Chapter 1 sections 1 to 13
SEMESTER – I PAPER-2
CLASSICAL MECHANICS AND SPECIAL THEORY OF RELATIVITY
MODULE-I
Mechanics of a single particle-conservation theorems-conservative forces-mechanics of system of particles-kinds of constraints-principle of virtual work-D’Alembert’s principle-difficulties caused by constraints.
Lagrangian formalism-generalised coordinates (GC)-Lagrange’s equation (L eq) for conservative holonomic systems-advantages of L formalism over Newtonian formalism-equivalence of L eq and Newton’s equations.
Central forces-two body problem simplified to one body problem-Rutherford’s scattering-equation for orbit acted upon by central force (CF)-equation of motion of a particle which passes through the centre of force of CF-Kepler’s laws.
Calculus of variations- Euler Lagrange equation-shortest distance between two points.
Hamiltonian formalism-cyclic coordinates (CC)-generalised momentum conjugate to a CC -conservation of energy-Hamiltonian as a constant of motion-conservation of linear and angular momenta-symmetry properties-physical significance of Hamiltonian-Hamilton’s equations for conservative holonomic systems-advantages of Hamilton’s formalism over L formalism-phase space-Liouville’s theorem.
Variational principles-Hamilton’s principle-principle of least action-its alternative form in terms of arc length of particle’s trajectory-advantages of H principle over L and H formalisms-linear harmonic oscillator.
Canonical transformations (CT)-definition and properties of CT-Legendre transformations-examples of CT-CT and fundamental Poisson’s brackets-CT leading to CC-linear harmonic oscillator-freely falling body-identity and exchange transformations –infinitesimal CT-CT leading to both constant GC and generalised momenta-generating functions.
Poisson’s brackets (PB) and their properties-invariance of PB under CT-Hamilton’s equations in PB-fundamental PB in CT -forming new constants of motion-PB with Hamiltonian-Jacobi’s identity-identifying constants of motion-PB and components of linear and angular momenta-classical and quantum PB.
MODULE - II
Hamilton-Jacobi formalism (HJ)-HJ equation-Hamilton’s principal and characteristic functions-linear harmonic oscillator-Kepler’s equations.
Action angle variables formalism-time periods of periodic motion-linear harmonic oscillator-Kepler’s equations.
Dynamics of a rigid body (RB)-degrees of freedom of a rigid body-inertial forces in a rotating frame-transformation matrix-rate of change of a vector-Coriolis force-river flow-freely falling body-Focault’s pendulum-atomic nuclei-inertia tensor-properties and diagonalisation-principal axes of rotation and principal moments of inertia-Eulerian angles-angular momentum and kinetic energy of a RB-Euler’s equations for (a) motion in a force field and (b) force free motion of a RB-rotation of angular velocity vector in space-precession of freely rotating body-rotation of earth-force free motion of symmetric top.
Special theory of relativity-Michelson Morley experiment-Lorentz transformations (LT) of space and time-Lorentz Fitzgerald contraction-time expansion and its experimental verification-proper length and proper time-addition of velocities and accelerations.
Relativistic Mechanics-transformation of velocity and acceleration-relativistic mass-mass energy equivalence and its experimental verification-examples of mass energy conversion-e+-e- annihilation and nuclear binding energy transformation of mass, density and force-Lorentz transformation equations for momentum and enegry and their similarity with LT equations for space and time-particles with zero rest mass -relativistic kinetic energy and total energy-Einstein’s equation.
Minkowski’s space (MS)-world space, world points and world lines-Doppler’s effect (DE) and relativistic DE-experimental verification.
Lorentz invariance of (a) four dimensional volume element (b) length of the space time interval and differential interval and (c) E2-p2c2. space like and time like intervals-geometrical interpretation of LT as a rotation of coordinate axes in MS.
Relativistic Lagrangian and relativistic Hamiltonian.
Relativistic equations of motion.
Text and Reference Books:
1. Classical Mechanics by Herbert Goldstein. Chapters: 1-5,6,7,8 and 9.
2. Classical Mechanics by N.C. Rana and P.C. Joag. Chapters: 1-6,8,9,10 and 12.
3. Classical Mechanics by J.C. Upadhyaya. Chapters: 1-7.
4. Introduction to Special Relativity by Robert Resnick. Chapters: 1-3.
5. Relativity by J.C. Goyal and K.P. Gupta. Chapters: 1-4.
SEMESTER – I PAPER – 3
QUANTUM MECHANICS - I
MODULE – I
Introduction: Wave particle duality – physical significance of the wave function – wave packets – states with minimum uncertainty product – time evolution of the system – superposition principle – wave function of a particle having definite angular momentum – Heisenberg’s uncertainty principle – complementary principle.
(B.J. : Ch. 2 ; G.K.S.S.: Ch. 2)
Schrodinger’s wave equation: time dependent Schrodinger’s wave equation – conservation of probability – continuity equation – expectation values of dynamical variables – Ehrenfest’s theorem – time independent Schrodinger’s wave equation – stationary states – admissible wave functions – energy quantisation – properties of eigen functions – Dirac’s delta function.
(B.J. : Ch. 3 Sec.1-6, Appendix A; G.K.S.S.: Ch. 2)
Applications of time independent Schrodinger’s wave equation to one-dimensional problems : free particle – potential step – potential barrier – infinite square well – linear harmonic oscillator.
(B.J. : Ch. 4 ; G.K.S.S.: Ch. 4.1,5-9)
Formalism of quantum mechanics: state of the system – dynamical variables and operators – adjoint of an operator – Hermitian operators – properties of Hermitian operators – derivation of Heisenberg’s uncertainty principle.
(B.J. : Ch. 5 Sec.1-4,7; G.K.S.S.: Ch. 8.10,10-1to14)
Angular momentum and quantum mechanics: orbital angular momentum – commutation relation for orbital angular momentum – eigen values and eigen functions of LZ and L2 – rigid rotator. Elementary theory of spin angular momentum: spin angular momentum – spin magnetic moment and spin orbit interaction – Pauli’s spin matrices.
(B.J. : Ch. 6 Sec.1-4,8; G.K.S.S.: Ch. 8.16, 10-6 to10, 12.1to 5 )
Text books: (1) Introduction to Quantum Mechanics - B. H. Bransden and C. J. Joachain
(2) Quantum Mechanics - Gupta, Kumar and Sharma
MODULE – II
Applications of time independent Schrodinger’s wave equation to three-dimensional problems: free particle – separation of Schrodinger’s wave equation in Cartesian co-ordinates – three dimensional harmonic oscillator – central potentials – separation of Schrodinger’s wave equation in spherical polar co-ordinates – hydrogen atom.
(B.J. : Ch. 7 Sec.2, 5 and 16; G.K.S.S.: Ch. 5.1,6 and 11)
Time independent perturbation theory: non degenerate states and degenerate states – application to linear Stark effect.
Variational method – ground state energy of the hydrogen atom – helium atom.
W.K.B. method – barrier penetration – alpha decay.
(B.J. : Ch. 8 Sec.1-4; G.K.S.S.: Ch. 9.1-5.1 (B))
Text books: (1) Introduction to Quantum Mechanics - B. H. Bransden and C. J. Joachain
(2) Quantum Mechanics - Gupta, Kumar and Sharma
Text and Reference Books:
(1) Quantum Mechanics – L.I. Schiff.
(2) Quantum Mechanics – A.P. Messaiah
(3) Quantum Mechanics – E. Merzbacher
(4) Quantum Mechanics – A.K. Ghatak and S. Lokanadhan and
(5) A Text Book of Quantum Mechanics – P.M. Mathews and K. Venkatesan.
SEMESTER – I PAPER – 4
ELECTRONIC DEVICES AND CIRCUITS
MODULE I
Network theorems:- Thevenin theorem, Norton’s theorem and maximum power transfer theorem.
Semiconductor Devices:- Tunnel diode, LDR, Photo diode, Solar cell, LED.
UJT- characteristics and relaxation oscillator. JFET and MOSFET – construction and characteristics – and their applications. JFET as common source amplifier.
BJT – CE amplifier – voltage gain, input and output resistance, graphical analysis and analysis using h-parameter equivalent circuit.
Feedback Amplifiers : Feedback concept, types of feed back, general characteristics of negative feedback in amplifiers, voltage series feedback, current series feed back and voltage shunt feedback.
Digital Electronics: (Combinational Logic)The transistor as a switch, OR, AND and NOT gates – NOR and NAND gates – Ex OR gate. Boolean algebra and Logic implementation. Decoders and Encoders, Multiplexers and De multiplexers.
MODULE II
Digital Electronics: (Sequential Logic) Flip-Flops, one bit memory – RS flip-flop, JK flip-flop, JK – master slave flip-flop, T flip-flop. Modulo N counters.
Operational Amplifiers: Ideal Operational amplifier. Op. Amp. architecture- differential stage, gain stage, dc level shifting and output stage. Practical inverting and Non inverting Op. Amp configurations, voltage follower.
Op. Amp parameters – input offset voltage ( Vio) input bias current (Iio),Output offset voltage, Common Mode Rejection Ratio(CMRR), Slew rate, Op. Amp. Open loop gain
Op. Amplifier applications:- Summing, scaling and difference of input voltages, Integrator and Differentiator. RC phase shift Oscillator. Comparators. Window -comparator, Schmitt trigger, Astable and monostable multivibrators. Voltage regulators – fixed regulators and adjustable voltage regulators.
Text and Reference Books :
1. Electronic devices and circuits Theodore F. Bogart, Jr.
2. Electronic devices and circuits Allen Mottershead.
3. Digital principles and Applications - A.P. Malvino and D.P. Leach.
SEMESTER – II PAPER – 1
ATOMIC AND MOLECULAR PHYSICS
MODULE - I
Spectra of alkali elements- Different series in alkali spectra, Ritz combination principle, Spin-orbit interaction, Doublet structure in alkali spectra, transition rules, intensity rules.
Spectra of alkaline earths, Coupling schemes, interaction energy levels in L-S coupling and j-j coupling, singlet and triplet series in two valance electron systems. Spectrum of helium atom.
Fine and hyperfine structure of spectral lines—fine structure of hydrogen lines, Lamb shift, experimental determination of Lamb shift, hyperfine structure—experimental study and interpretation, measurement of nuclear spin.
Effect of electric and magnetic fields on the spectrum of an atom—Zeeman effect—classical interpretation of Normal Zeeman effect, Vector atom model and Zeeman effect, Vector atom model anomalous Zeeman effect, Paschen – Back effect, quantam mechanical treatment of Zeeman and Paschen-Back effect, Lande’s g-factor for two valance electron system—L-S coupling and j-j coupling, Stark effect of one electron atom.
Scope: Elements of Spectroscopy by Gupta, Kumar & Sharma
Section-I Cha. 6 Sec. 1, 2,4,5,6,7,12,13,14,17 & 19
Section-I Cha. 7 Sec. 1,2,5,7,9 & Cha. 9 Sec. 1,2,3,4,5,6,7,11,12
Text and Reference Book:
Introduction to Atomic Spectra by H.E. White, McGraw Hill Publ.
MODULE - II
Molecular spectra of diatomic molecules-regions of the spectrum, Pure rotational spectra—salient features of rotational spectra, the molecule as a rigid rotator, diatomic molecule as a non rigid rotator, determination of bond length and moment of inertia, isotopic effect in rotational spectra, Vibrational spectra-- diatomic molecule as a harmonic oscillator, fine structure of rotation-vibration bands, Electronic transitions and Frank-Condon principle.
Raman spectra—classical and quantum theory of Raman effect, vibrational Raman spectra, pure rotational Raman spectra, vibrational-rotational Raman spectra, structure determination from Raman & infra red spectroscopy.
Scope: Elements of Spectroscopy by Gupta, Kumar & Sharma
Section IV 1.2, 2.1, 2.2,2.3, 3.1,3.3, 3.4, 5.1,5.2.
Section IV 4.0,1,2,3,4.
Text and Reference Book:
Fundamentals of Molecular Spectroscopy, C.N. Barwell, Tata-McGraw Hill.
SEMESTER – II PAPER – 2
QUANTUM MECHANICS – II
MODULE – I
Time dependent perturbation theory – transition to continuum – Fermi’s golden rule – constant perturbation, harmonic perturbation – adiabatic and sudden approximations.
Text Book: Chapter 9 – (Relevant Portion) – Introduction to Quantum Mechanics by B.H. Bransden & C.J. Joachain.
Semi classical theory of radiation: Radiative transitions in atoms placed in an electro magnetic field – transition probabilities for absorption and emission – dipole transition – selection rules for allowed transition – forbidden transitions – statistical approach for absorption, spontaneous and induced emission – Einstein A&B coefficients.
Text Books: 1) 11.1 to 11.3 (Partly), 11.4 Introduction to Quantum Mechanics by B.H.Bransden & C.J.Joachain.
2) 9.13 to 9.15 – A text book of Quantum Mechanics – P.M. Mathews & K. Venkatesan.
Matrix formulation of quantum mechanics: Linear Vector Spaces – Hilbert Space, linear operators, linear transformation, matrix representation of an operator and wave function - orthonormality of wave functions. Dirac’s Bra and Ket formalism. Schroedinger’s equation and the eigen value problem – energy representation. One dimensional harmonic oscillator – solution by matrix mechanics.