Contents

**HNB Garhwal M.Sc Physics Syllabus 2018| All Semester Master In Science Exam Syllabus**

## Introduction

Now as you have taken admission in the course whihc you like the most for your higher education. Now is the time that you must know about what you need to study for your course. You must be worried about the syllabus as you are new to it and must be tensed how to complete it in such a short interval of time. All things considered, that is the manner by which one can progress toward becoming expert in the concerned course one has pursueed from this college. On the off chance that you watch out for this page which is about HNBGU Garhwal University Exam Syllabus 2018 for the student those who had opted for the M.SC and different courses. We are here providing here the syllabus for the M.Sc Physics there are various subject in this course but for the time now we are providing you the syllabus for the Physics.

## HNB Garhwal M.Sc Physics Syllabus 2018

This course have traverse of 3 years and isolated in 6 semester and every one of the competitors the individuals who are as of now assuming or who had connected for the course they presently be searching for the syllabus for it. Despite the fact that the exam dates are not discharged yet and thee exam are thing which occur in at regular intervals. Beneath you get the subtle elements syllabus so experience the article underneath.

###### Syllabus For Semester 1

**Mathematics**

- Functions of a complex variable.
- Analytic functions,
- Cauchy-Riemann equations,
- integration in the Complex plane,
- Cauichy’s theorem,
- Cauchy’s integral formula.
- Liouville’s theorem.
- Moretra’s theorem.
- Proof of Taylor and Laurent expansions.
- Singular Points and their classification.
- Branch Point and branch Cut. Riemann sheets.
- Residue theorem.
- Integrals involving branch point singularity. (5+8 lectures)
- Linear vector spaces, subspaces, Bases and dimension, Linear independence and

orthogonality of vectors, Gram-Schmidt orthogonalisation procedure. Linear operators. - Matrix representation.
- The algebra of matrices. Special matrices. Rank of a matrix.
- Elementary transformations.
- Elementary matrices. Equivalent matrices. Solution of linear

equations.

**Classical Mechanics**

- Review of Lagrangian and Hamiltonian formalisms in different systems. Legendre transforms.
- Hamilton’s canonical equations and their applications. Lagrangian and Hamiltonian for

relativistic particles - Canonical transformations and some applications. Infinitesimal Canonical transformation.
- Integral invariant of Poincare. Lagrange and Poisson brackets and their applications.
- Liouville’s theorem.
- Hamilton-Jacobi equation for Hamilton’s principle and characteristis function and their

apllication. - Rigid body motion. Heavy symmetrical top with one pont fixed on the axis. Fast and sleeping top.
- Deformable bodies. Strain and stress tensor. Energy of elastic deformation.
- Fluid dymnamis. Permanancy of vortices. Navier-Stokes theorem.

**Quantum Mechanics**

- Linear vector space – State space, Dirac notation and Representation of State Spaces,

Concept of Kets, Bras and Operators, Expectation Values - State function and its interpretation, Expectation Values, Expansion of a State Function and Superposition of states.
- Matrix Representation of State Vectors and operators, Continuous Basis. Relation between a State Vector and its Wave function, Operator Method, Coherent States.
- Schrödinger equation and its applications- In one dimensional consideration- Particle in one-dimensional potential well and its energy states; Linear harmonic oscillator; Solutions of different one-dimensional barriers (finite and infinite width) and penetration problems. In three dimensional consideration-Free particle wave function; Motion of a charged particle in a spherically symmetric field
- Approximation methods – Time-independent perturbation theory for non-degenerate and degenerate states. Applications: Anharmonic oscillator, Helium atom, Stark effect in hydrogen atom, Variational methods: Helium atom.

**Classical Electrodynamics**

- Inhomogeneous wave equation: it’s solution. Lineard-Wiechert potentials.
- Field of a uniformly moving charge.
- Fields of an accelerated charge. Radiation from a charge at low velocity. Radiation from a charge at linear motion and circular motion or orbit.
- Bremsstrahlung- Cerenkov radiation. Relativistic electrodynamics. Covariant form of EM

equations. Transformation law for the EM field. - Classical theory of electron: Radiation reaction from energy conversation: Lorentz theory Self force.

**Solid State Physics**

- Crystalline and amorphous solids. The crystal lattice. Basis vectors. Unit cell. Symmetry operations.
- Simple crystal structures: FCC, BCC, Nacl, CsCl, Diamond and ZnS structure,

HCP structure. (4 lectures) - X-ray diffraction by crystals. Laue theory. Interpretation of Laue equations. Bragg’s law.

Reciprocal lattice. Ewald construction. Atomic scattering factor. - Types of bonding. The van der waals bond. Cohesive energy of inert gas solids. Ionic bond. Cohesive energy and bulk modulas of ionic crystals.
- Vibrations of one-dimensional monatomic and diatomic lattices. Infrared absorption in

ionic crystals (one-dimensional model). Normal modes and phonons. - Magnetic properties of solids. Diamagnetism, Langevin equation. Quantum theory of

paramagnetism. Curie law. Hund’s rules. Paramagnetism in rare earth and iron group ions.

**Electronics**

- Passive Networks:

Synthesis of two terminal reactive networks – Driving point impedance and admittance,

Four-terminal two-port network – parameters for symmetrical and unsymmetrical networks; image, iterative and characteristic impedances; propagation function; lattice network. - High Frequency Transmission Line:

Distributed parameters; primary and secondary line constants; Telegraphers’ equation;

Reflection co-efficient and VSWR. - Semiconductor Devices:

p-n junction physics- Fabrication steps; thermal equilibrium condition; depletion

capacitance; current-voltage characteristics. Characteristics of some semiconductor devices- BJT, JFET, MOS, LED, Solar cell, Tunnel - Active Circuits:

Transistor amplifiers- Basic design consideration; high frequency effects; video and pulse

amplifier; resonance amplifier; feedback in amplifiers - Harmonic self-oscillators – Steady state operation of self-oscillator; nonlinear equation of self- oscillator; examples.

**Atomic Spectroscopy**

- General discussion in Hydrogen spectra, Hydrogen-like systems, Spectra of monovalent

atoms, quantum defect, penetrating and non-penetrating orbits, introduction to electron spin, Lambshift. - Spectra of divalent atoms: Singlet and triplet states of divalent atoms, L-S and j-j coupling, complex spectra, equivalent electrons and Pauli exclusion principle.
- Hyperfine structure in spectra of monovalent atoms, origin of X-rays spectra, screening

constants, fine structure of X-ray levels. - Lasers in Spectroscopy: Broadening of spectral lines, Doppler-free spectroscopy, excitation spectroscopy.

**Nuclear Physics**

- General properties of nuclei : Introduction, parity and isospin of nuclei, muonic atoms and electron scattering.
- Two-nucleon problem and nuclear forces: Deuteron ground state, excited states, two nucleon scattering, n-p scattering, partial wave analysis, phase-shift, scattering length, scattering (qualitative discussion), charge symmetry and charge independence of nuclear forces.
- Nuclear models : Need for nuclear models, Fermi gas model, spherical shell model.
- Nuclear reactions : Direct and compound nuclear-reactions, experimental verification of Bohr’s independence-hypothesis, resonance reactions,
- Particle accelerators : Pelletron, tandem principle, Synchrotron and synchrosyclotron,

colliding beams, threshold energy for particle production.

**Syllabus For Semester 2**

**Mathematics 2**

- Fourier and Laplace transforms. Inverse transforms. Covolution theorem. Solution of

ordinary and partial differential equations by transform methods. - Green’s functions for ordinary and partial differential equations of mathematical physics.

Integral equations. Fredholm and volterra equations of the first and second kinds. - Tensor analysis, Coordinate transformations, scalars, Covariant and Contravariant tensors.
- Addition, Subtraction, Outer product, Inner product and Contraction. Symmetric and

antisymmetric tensors. Quotient law. Metric tensor. Conjugate tensor. Length and angle

between vectors. Associated tensors.

**Relativity and Cosmology**

- Review of special theory of relativity: Poincare and Minkowski’s 4-dimensional formulation, geometrical representation of Lorentz

transformations in Minkowski’s space and length contraction. - Review of tensor calculus: Idea of Euclidean and non-Euclidean space, meaning of parallel transport and covariant.
- Einstein’s field equations: Inconsistencies of Newtonian gravitation with STR, Principles of equivalence, Principle of general covariance, Metric tensors and Newtonian Gravitational potential, Logical steps leading to Einstein’s field equations of gravitation.
- Applications of general relativity: Schwarzschild’s exterior solution, singularity, event horizon and black holes, isotropic coordinates.
- Gravitational Collapse and Black Holes (Qualitative): Introduction, Qualitative discussions on: White Dwarfs, Neutron stars and Black Holes, Static Black Holes
- Cosmology: Introduction, Cosmological Principles, Weyl postulates, Robertson-Walker metric (derivation is not required) universe, Cosmological red shift, Hubble’s law. Olber’s Paradox.

**Quantum Mechanics 2**

- Generalised angular momentum- Infinitesimal rotation, Generator of rotation,

Commutation rules, Matrix representation of angular momentum operators, Spin, Pauli spin matrices. - Symmetries- Symmetries, Invariance principle and Conservation laws, Space translation,

Time translation, Space rotation. - Approximation methods- Time-independent perturbation theory for non-degenerate and

degenerate states, Application: anharmonic oscillator, Helium atom, Stark effect in

hydrogen atom, Variational methods: Helium atom. - Scattering theory- Scattering of a particle by a fixed centre of force. Scattering amplitude differential and total cross sections. Scattering by a hard sphere and potential well. Integral equation for potential scattering.

**Classical Electrodynamics**

- Scattering: free and bound electron. Dispersion and absorption: Lorentz electro magnetic theory.
- Magnetohydrodynamic (MHD) equations, magnetic, viscosity, pressure, Reynold number,

etc. MHD waves. Alfven waves and velocity, Hartmann flow and Hartmann number. - Orbit theory of drift motions in a plasma. Pinch effect. Instability in pinched plasma column. Plasma oscillations, short wavelength of plasma oscillation and Debye screening length.
- Propagation of EM waves through plasma. Effect of external magnetic field on wave

propagations: ordinary and extraordinary rays. - Multipole radiation.

**Solid State Physics**

- Quantized free electron theory. Fermi energy, wave vector, velocity and temperature,

density of states. Electronic specific heats. Pauli spin paramagnetism. Sommerfeld’s model for metallic conduction. - Intrinsic and extrinsic semiconductors. carrier concentration and Fermi levels of intrinsic

and extrinsic semi-conductors Bandgap. - Energy bands in solids. The Bloch theorem. Bloch functions. Review of the Kroning-

penney model. - The tight binding model. The fermi surface. Electron dynamics in an electric field. The effective mass. Concept of hole.
- Superconductivity, Survey of important experimental results. Critical temperature.

Meissner effect. Type 1 and type ii superconductors. Thermodynamics of superconducting transition.

**Electronics**

- Op-Amp Circuits: Characteristics of ideal and practical op-amp; Nonlinear amplifiers using op-amps- log amplifier
- Voltage Regulators: Series op amp regulator, IC regulator, Switching regulators.
- Elements of Communication Electronics: Principles of analog modulation- linear and

exponential types - Modulation techniques in some practical communication systems: AM and FM radio, VSB

AM and QAM technique in TV broadcasting. - Digital Circuits: Logic functions; Logic simplification using Karnaugh maps; SOP and

POS design of logic circuits; MUX as universal building block. - RCA, CLA and BCD adder circuits; ADD-SHIFT and array multiplier circuits. RS, JK and MS-JK flip-flops; registers and counters (principle only).

**Advance Optics**

- Basic Laser Theory
- Basic Laser Systems: Gas Laser: CO2 laser, Solid State Laser: Host material and its characteristics, doped ions.
- Laser Beam Propagation: Laser beam propagation, properties of Gaussian beam, resonator, stability, various types of resonators
- Nonlinear Optics: Origin of nonlinearity, susceptibility tensor, phase matching, second harmonic generation.
- Holography: Importance of coherence, Principle of holography and characteristics, Recording and reconstruction
- Transient effect: Principle of Q-switching, different methods of Q-switching, electro-optic Q-switching.
- Fibre optics: Dielectric slab waveguide, modes in the symmetric slab waveguide, TE and TM modes, modes in the asymmetric slab waveguide dispersion and distortion in the slab waveguide, integrated optics components
- Detection of optical radiation: Human eye, thermal detector (bolometer, pyro-electric), photon detector (photoconductive detector, photo voltaic detector and photoemissive detector)

**Nuclear Physics**

- Beta and Gamma decay : Fermi’s theory of beta decay, allowed and forbidden transitions, selection rules, non-conservation of parity in beta decay, direct evidence for the neutrino,
- Energy loss of charged particles and gamma rays : Mechanism, Ionization formula,

Stopping power and range, radiation detectors. - Reactor Physics : Slowing down of neutrons in a moderator, average log decrement of

energy per collision, slowing down power, moderating ratio. - High energy physics : Types of interaction in nature-typical strengths and time-scales, conservation laws, quark hypothesis, charm, beauty and truth, gluons, quark- confinement, asymptotic freedom.

###### Syllabus For Semester 3

**Statistical Mechanics**

- Scope and aim of statistical mechanics. Transition from thermodynamics to statistical

mechanics. Review of the ideas of phase space, phase points, Ensemble. - Stationary ensembles: Micro canonical, canonical and grand canonical ensembles.

Partition function formulation, Fluctuation in energy and particle. - Density matrix: Idea of quantum mechanical ensemble. Statistical and quantum

mechanical approaches, Properties, Application to a free particle in a box, an

electron in a magnetic field. - Distribution functions. Bose-Einstein and Fermi-Dirac statistics. General equations of

state for ideal quantum systems.

**Quantum Mechanics**

- The Klein Gordon equation. Covariant notations. Negative energy and negative probability density.
- The Dirac equation. Properties of the Dirac matrices. The Dirac particle in an external

electromagnetic field. - Covariant form of the Dirac equation. Lorentz covariance of the Dirac equation. Boost as

hyper rotation Boost, rotation, parity and time reversal operation on the Dirac wave function. - Conjugate Dirac spinor and its Lorentz transformation. The γ 5

matrix and its properties. - Boosting the wave function from the rest frame. Plane wave solutions of the Dirac equation and their properties.
- Dirac’s hole theory and charge conjugation. Feynman-Stuckelberg interpretation of

antiparticles. - Foldy-Wuthuysen transformations: Free particle transformation. The general transformation.
- The Hydrogen atom.

**Group Theory**

- Abstract group theory: Definition. Group postulates. Finite and infinite groups, order of a group, subgroup; rearrangement theorem, multiplication table. Cosets, Lagrange’s theorem. Order of an element.
- Representation theory: Definition of representation. Faithful and unfaithful representations. Invariant subspaces and reducible representations.
- Continuous group: Infinite groups. Discrete and continuous groups, mixed continuous group. Topological and Lie groups. Axial rotation group SO(2).
- Application in Physics: Group of Schrodinger equation.

**Computer Application In Physics**

- Computer fundamentals: Functional units-CPU, Memory, I/O units; Information representation- integral and real number representation
- Computer Software and Operating Systems: System software and application software; Translator programs; Loaders and linkers.
- Elements of C Programming Language: Algorithms and flowchart; Structure of a high level language program; Features of C language, Input and output statements; conditional statements and loop statements; arrays; functions;

**Solid State Physics Special**

- Diffraction of x-rays by crystals – scattering of x-rays by an atom and by a three dimensional crystal. Laue interference function, Bragg equation. Ewald construction. Width of diffraction maxima.
- Crystal elastivity – Generalised Hooke’s law strain energy function cauchy relations.

Propagation of elastic waves through cubic crystals. - Language and use of second quantization formalism: application to the free electron gas,

Band electrons in a magnetic field, Fermi surface and its experimental determination - Energy bands: Different methods of calculation of energy bands in solids viz., Nearly free electron model, orthogonalised plane wave (OPW) method and pseudo-potential methods.
- General magnetism: Magnetic susceptibility tensor, quadratic representation, correlation of principal susceptibilities with crystallographic axes in different crystal systems using magnetic ellipsoid.
- Paramagnetism: Van Vleck expressions of susceptibility, quantum mechanical derivation of Langevin, Debye formula, Crystal field Hamiltonian, Steven’s operators, Operator equivalent method, splitting of 3d ions in octahedral and tetrahedral field, Orgel diagram.

**Appllied Crystallography in Material Science**

- Noncrystalline and semicrystalline states, Lattice. Crystal systems, unit cells. Indices of lattice directions and planes. Coordinates of position in the unit cell, Zones and zone axes. Crystal geometry.
- Introduction to materials, Classification of materials: Crystalline & amorphous materials,
- Preparation techniques of materials
- Preparation of materials by different techniques: Single crystal growth, zone refining,
- Synthesis of nanomaterials: Top down and bottom up approaches of synthesis of nano-structured materials, nanorods.
- Phase transition in materials, Solid solutions, Phases, Thermodynamics of solutions, Phase rule, Binary phase diagrams, kinetics of solid reactions.

**Syllabus For Semester 4**

**Statistical Mechanics**

- Ideal quantum systems: Properties of ideal Bose gas: Bose-Einstein condensation: Transition in liquid He4 Superfluidity in He4 Photon gas: Planck’s radiation law. Phonon gas: Debye’s theory of specific heat of solids.
- Properties of ideal Fermi gas: Review of the thermal and electrical properties of an ideal electron gas. Landau levels, Landau diamagnetism. White dwarf and Neutron stars.
- Strongly interacting systems: Ising model. Idea of exchange interaction and Heisenberg Hamiltonian. Ising Hamiltonian as a truncated Heisenberg Hamiltonian.
- Phase transition: General remarks. Phase transition and critical phenomena. Critical indices. Landau’s order parameter theory of phase transition. (3 lectures)
- Fluctuations. Thermodynamic fluctuations. Spatial correlations in a fluid. Brownian motion: Einstein-Smoluchowski’s theory.

**Advance Quantum Mechanics 2**

- Concepts of fields. Lagrangian dynamics of Classical fields. Derivation of the Euler-Lagrange equation from Hasmilton’s variational principle. Lagrangians and equations of motion of fundamental fields.
- Noether’s theorem. Invariances. Conserved currents and charges. Energy-momentum tensors and energy of fields.
- Canonical quantization and particle interpretation of the real Klein-Gordon field. Fock space of bosons. Energy of the real Klein Gordon field. Normal ordering.
- Introduction of antiparticle. Charge of quantum complex Klein-Gordon field.
- Canonical quantization and energy of the Dirac field. Anti-commutators. Pauli principle.
- Coulomb gauge quantization and energy of the Electromagnetic field. (4 lectures)
- A comparison between non-covariant and covariant quantization of the electromagnetic field.
- Features of covariant quantizations : Derivation of equal-time commutators between the

components of fields and canonically conjugate momentum fields, (Derivation of energy

operator not needed)

**Molecular Spectroscopy**

- Born-Oppenheimer approximation and separation of electronic and nuclear motions in

molecules. Band structures of molecular spectra. - Microwave and far infrared spectroscopy: Energy levels of diatomic molecules under rigid rotator and non-rigid rotator models.
- Infrared spectra : Energy levels of diatomic molecules under simple harmonic and

anharmonic (no deduction necessary for this one) models. Selection rules and spectral

structures. - Raman spectroscopy. Rotational, Vibrational, Rotational-Vibrational Raman spectra. Stokes and anti stokes Raman lines. Selection Rules.
- Vibrational spectra of poly atomic molecules. Normal modes. Selection rules for Raman and infrared spectra.
- Basic aspects of photo physical processes: radiative and non-radiative transitions; fluorescence and phosphorescence; Kasha’s rules. Nuclear Magnetic resonance spectroscopy.
- Application of group theory to spectroscopy.

**Astrophysics**

- Introduction: Astrophysics and Astronomy, Celestial coordinate systems (Sun-Earth system, Galactic Coordinate system).
- Stellar Structure and Evolution: Star formation, Stellar Magnitudes.

ii) Gravitational energy, Virial theorem, Equations of stellar structure and evolution.

iii) Pre-main sequence evolution, Jeans criteria for star formation, fragmentation and

adiabatic contraction. - Nuclear Astrophysics: Thermonuclear reactions in stars, pp chains and CNO cycle, Solar Neutrino problem, subsequent thermonuclear reactions.
- Stellar Objects & Stellar Explosions: Qualitative discussions on: Galaxies, Nabulae, Quasars, Brown dwarfs, Red Giant Stars.
- Gravitational Collapse and relativistic Astrophysics: Newtonian theory of stellar equilibrium, White Dwarfs, Electron degeneracy and equation of

States, Chandrasekhar Limit.

**Computer Application In Physics**

- CPU- programmers model; instruction set and addressing modes of a generic CPU; RISC and SISC; Storage System- primary and secondary memory; semiconductor, magnetic and opticalmemory; cache memory; virtual memory; memory management; IO Units – keyboard, mouse. Internet- structure, TCP/IP protocol, internet services; Introduction to WWW.

2. Representation of integers and real numbers; Accuracy, range, overflow and underflow of number representation

So now you have the detailed syllabus about the M.Sc Physics of the HNB Garhwal university we are soon going to update more and more syllabus of the various subjects so keep in touch with us. If you have any queries or view about the article then please comment in the comment box.