Structure of Syllabus :
1. There will be Three Theory Papers Number I, II & III each of 100 Marks.
2. There Lecture-periods of 1 hour, each per paper per week are to be assigned to complete the syllabus
of relevant theory paper.
3.
There will be Three Practicals of Three hours per week. Each
Practical carrier 50 Marks and number of
student in a single batch should not
exceed 10 (Ten).
4. University Examination Pattern :
Theory Duration Marks
Paper-I 3 Hours 100
Paper-II 3 Hours 100
Paper-III 3 Hours 100
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Total Marks (Theory) 300
--------
Practicals Duration Marks
Experiment-I 3 Hours 50
Experiment-II 3 Hours 50
Experiment-III 3 Hours 50
--------
Total Marks (Practicals) 150
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Note : (1) Syllabus of each Question Paper has been divided into FIVE UNITS.
(2) One question must be set from each unit with internal option only.
(3) As far as possible, proportionate weightage of marks should be given to various
sub-units/topics from each unit.
(4) Each question will have normally 3 subquestions (a), (b), & (c) detailed as under :
(a) Theory question
(b) Theory question / Application 16 Marks
(c) Problem / Example / Application 04 Marks
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Total 20 Marks
MATHEMATICAL METHODS
Unit - 1 (20 Lecture-Periods : 20 Marks)
(a) Function of a Complex Variable :
(1) Analytic functions (2) Contour Integrals (3) Laurent series (4) Residue theorem (5) Methods
of Finding Residues (6) Evaluation of Definite Integrals by use of the Residue theorem
(7) The point of Infinity, Residue of Infinity (8) Mapping (9) Some Applications of conformal mapping
(b) Integral Transforms :
(1) Introduction (1) Laplace Transforms (2) Solution of Differential Equation by Laplace Transforms (3)
Fourier Transforms (4) Convolution : Parseval's Theorem (5) Inverse Laplace Transform (Bromwich
Integral) (6) Dirac Delta function (7).
Basic reference :
Mathematical methods in Physics Sciences by M.L. Boas 2nd edition, John Wiley & Sons,1999.
Chapter 14 and 15. For article b(7) also see G.B. Arfken and J.H. Weber.
(c) Non-linear Differential Equations and Boundary Value Problems :
Boundary value problems in Physics (4.1) Boundary value problems and Series solution (4.2) Examples
of boundary value problems (exclude example 4 & similarly done in electrodynamics) (4.3) Eigen value
eigen function & sturm-Liouville problem (4.4) Hermition Operators Their eigen value and eigen
function (4.5)
Basic reference :
Mathematical physics by P.K. Chattopadhyay, 1990 New age international (P) Ltd., New Delhi,
Chapter 4 (Reprint 2001).
Unit - 2 (20 Lecture-Periods : 20 Marks)
(a) Tensor analysis :
Introduction, Definition, Contra variant vector, Covariant vector, Definition of Tensors of rank two,
addition & subtraction of tensor, summation convention, symmetry - antisymmetry of second rank
tensor (2.6) Contraction, Direct product (2.7) Quotient rule (2.8) Pseudo tensors Dual tensor
Levi-civita symbol, irrducible tensor (2.9), Non cartesian tensors, Matro tensor christoffel symbols,
christoffel symbols asdervatives of matric tensor, convariant derivative (2.10) Tensor derivative
operators (2.11).
Basic reference :
Mathematical Methods for Physicist by G.B. Afrken & H.J. Weber 5th Edition 2001 Harcot (India Pvt.
Ltd.)
(b) Some differential equations :
System of linear first order differential equations (3.6) Non-linear Differential Equations (3.7)
Basic reference :
Mathematical physics by P.K. Chattopadhyay, 1990, New age international (P) Ltd., New Delhi.
Chapter 3 (Reprint 2001).
(c) Group Theory :
Group, subgroups, classes (8.1) Invariant, subgroups, factor groups (8.2) Homomorphism &
Isomorphism (8.3) Group representation (8.4) Reducible & Irreducible representations (8.5) Schur's
lemma, Orthogonality theorem (8.6) Character of representation, Character table (8.7) Decomposing a
reducible representation into Irreducible ones (8.8) Construction of representations (8.9) Lie groups &
Lie algebra (8.11) The Three dimensional rotation groups SO(3) (8.12) The special unitary groups
SU(2) and SU(3) (8.13) The homomorphism between SU(2) & SU(3) (8.13a) Some application of group
theory in physics (8.14) (application 4 classification of elementary particles).
Basic reference :
Mathematical physics by P.K. Chattopadhayay, 1990, New age international (P) Ltd., New Delhi.
Chapter 8 (Reprint 2001).
QUANTUM MECHANICS
Unit- 3 (20 Lecture-Periods : 20 Marks)
(a) Some exactly soluble Three-dimensional problem in quantum mechanics :
An isotropic oscillator (4.20) The isotropic oscillator (4.21) Normal modes of a coupled system of
particle (4.22)
(b) Approximation methods for stationary states :
Perturbation theory for Discrete level (5.1) Equation in various orders of perturbation theory (5.2) Non
degenerate case (5.3) The degenerated caseremovel of degeneracy (5.4) The effect of electrical field
on energy level of an atom (Stark effect) (5.5) Two electron atoms; The variation method (5.6) Upper
bound on ground state energy (5.7) Applications to excited state (5.8) Trial function; Linear in
variation parameters (5.9) Hydrogen molecule (5.10) Exchange interaction (5.11) The one dimensional
Schodinger (inclusive all cases & discussion relevant to perturbation theory / WKB method) (5.12) The
Bohr Sommefield quantum condition (5.13) The WKB solution of radial wave equation (5.14).
(c) Scattering theory :
The scattering cross-section, General considerations (6.1) Kinematics of scattering process;
Differential and Total cross-sections (6.2) Wave mechanical picture of scattering - The scattering
amplitude (6.3) Green functions : Formal expression for scattering Amplitude, The Born and Eikonal
Approximations (6.4) The Born Approximation (6.5) The validity of the born Approximation (6.6) The
Born series (6.7) The Eikonal Approximation (6.8).
Unit - 4 (20 Lecture-Periods : 20 Marks)
(a) Partial Wave Analysis :
Asymptotic Behavior of partial waves : phase shift (6.8) The scattering Amplitude in terms of
phaseshifts (6.9) The Differential and Total cross-sections, Optical theorem (6.10) Phace shifts :
relation to the potential (6.11) Potentials of finite range (6.12) Low energy scattering (6.13) Exactly
soluble problems (6.14) Scattering by a square well (6.15) scattering by a hard sphere (6.16)
scattering by a coulumb potential mutual scattering of two particles (6.17) Reduction of the two
body problem : The centre of mass frame (6.17) Transformation from centre of mass to Laboratory
frame of reference (6.18) collisions between identical particles (6.19).
(b) Operator methods in Quantum mechanics :
Representation, Transformations and Symmetries : quantum states, State vector and wave functions
(7.1) Hilbert space of state vectors : Dirac notatio (7.2) Dynamical variable and Linear operators (7.3)
Representations (7.4) continuous basis : The Schrodinger equation (7.6)
Degeneracy, labelling by
commuting observables (7.7) Change of
basis; Unitary transformations (7.8) Unitary transformation
induced by change of coordinate system : Translation (7.8) Unitary transformations induced by
Rotation of coordinate system (7.9) Algebra of rotation Generators (7.10) Transformation of
Dynamical variables (7.11) Symmetries and conservation laws Evolution with time (7.12) The
Schrodinger equation : General solution (9.1) Propagator (9.2) Relation of retarded propagator to the
Green's function of the Time - independent Schrodinger equation (9.3).
Basic reference for UNIT III & IV
A textbook of Quantum mechanics by P.M. Mathews and K. Venkatesan 1976 THM, New Delhi.
C-LANGUAGE
Unit - 5 (20 Lecture-Periods : 20 Marks)
(a) Overview of C:
Introduction (1.1) Importance of C (1.2) Sample C programme (1.3) Basic structure of C programmes
(1.4) programming style (1.5) Executing a "C" Programme (1.6).
(b) Constants, Variable and Data types :
Introduction (2.1) Character set (2.2) C tokens (2.3) Keywords and identifiers (2.4) constants (2.5)
variables (2.6) Data types (2.7) Declaration of variables (2.8) Assiging values to variables (2.9)
defining symbolic constants (Additional) : case studies (2.10).
(c) Operators and Expressions :
Introduction (3.1) Arithmetic operators (3.2) Relational operators (3.3) Logical operators (3.4)
assignment operators (3.5) Increment and Decrement operators (3.6) Conditional operators (3.7)
Bitwise operators (3.8) special operators (3.9) Arithmetic expressions (3.10) Evaluation of expressions
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