# Core Course Units

(135 hours of Practical and 45 hours of Library work)

**Objectives :**

- To train students with various modern and advanced experimental set-ups and orient them for research.
- Enhance the students’ understanding of various basic concepts in physics through measuring physical quantities.
- To develop the students’ soft skills such as writing scientific reports, learning through discussion and oral presentation of their scientific findings.
- To give an opportunity to the students to develop their experimental skills.

Introduction :

- In this course unit, the students are expected to work independently under the guidance of a senior staff assigned to them by the lecturer in - charge. Practical reports should be submitted in the form of a scientific paper. The students have to orally present an advanced experimental technique and one of their experiments, assigned by the lecturer in - charge, in a seminar to a panel of examiners.

**Evaluation :**

Continuous assessment on practical classes and reports | 40% |

Two end of semester examinations each of three hours duration | 40% |

Seminar presentations | 20% |

**Library Work**

**Objectives :**

- To encourage the students to learn through reading.
- To train the students to do literature survey on an assigned topic.
- To enable the students to access e-resources effectively.
- To develop soft skills such as reading, writing and oral presenting.

**Introduction :**

- In this course module, the students will carry out extensive literature survey on pre-assigned topics using e-resources and library. They are required to submit a report on the topic assigned to them and present it orally in a seminar to a panel of examiners.

**Evaluation :**

Report | 70% |

Seminar Presentation | 30% |

**Weightage: 75% Practical Physics IV and 25% Library Work.**

(45 hours of lectures and tutorials)

**Objectives:**

- To understand the basic principles of the Lagrangian and Hamiltonian formulation of classical mechanics and apply these principles to solve key problems.
- To introduce fundamental conservation laws to analyse mechanical systems.
- To introduce the concept and uses of four vectors in relativistic kinematics.
- To introduce Einstein's general relativity and cosmology.

Syllabus :

**Classical Mechanics:**

**Lagrangian mechanics:**

- Generalised coordinates, holonomic and non-holonomic constraints, Principle of least action and the derivation of Lagrange's equations of motion. Application of Lagrange's equations to solve simple problems.Conservation laws and symmetries in nature. Constraints and the method of Lagrange's undetermined multipliers, Generalized force and generalised momentum.

Central force problems:

- Vector treatment of motion of a particle in three dimensions, moving frames of reference, effects of the earth's rotation, motion under a central conservative force, the inverse square law, scattering cross-sections, motion of a charge particle in uniform and non-uniform electric and magnetic fields.

The two body problem:

- The centre of mass and relative coordinates, elastic collisions, scattering cross-sections in centre of mass and laboratory frames.

Rigid body motion:

- Rotational motion of a rigid body, moment of inertia, principal axes of inertia, gyroscopic motion.
- Small oscillations and normal modes

Hamiltonian Mechanics:

- Hamiltonian and the Hamilton's equations of motion, simple applications, ignorable coordinates, the symmetric top, symmetries and conservation laws.

Relativity:

**Special Relativity:**

- Review of postulates of special relativity and Lorentz transformation equations, four vectors, transformation of velocity, momentum and force using four vectors, field of a moving charge via force transformation, relativistic collision and decay problems.
- Transformation of wave number vector, radial and transverse Doppler effects in optics.

General Relativity

- Non-mathematical introduction to general relativity, Einstein's approach to gravity, black holes, concept of curved space time, experimental test of general relativity.
- Rudiments of cosmology.

**Evaluation:**

Two to three in-course assessment tests | 30% |

End of course written examination of three hours duration | 70% |

(Expected to answer four out of five questions) |

(45 hours of lectures and tutorials)

**Objectives:**

- To introduce the necessary characteristics of quantum theory and quantum mechanics in a more formal way, introducing a set of postulates.
- To enable students to solve the Time Independent Schrödinger Equation for simple quantum mechanical problems in one, two and three dimensions.
- To introduce algebraic methods in quantum mechanics and highlight the power of the technique involving ladder operators.
- Tointroduce the method of solving central field problems in spherical polar coordinates and the concept of angular momentum in quantum mechanics.
- To introduce matrix representation of operators and wavefunctions with emphasis on spinors.
- To introduce the quantum mechanical approach to the behaviour of identical particle systems.

**Syllabus :**

**Introduction:**

- Evidence of inadequacy of classical mechanics, Some necessary characteristics of quantum theory, The wave-particle duality, the wave function and probability amplitudes, wave packets, the Schrödinger equation, eigenvalue equations and their place in the quantum formalism, Calculation of expectation values of system parameters.

Solution of Schrödinger equation in some simple cases:

- One dimensional potential well and energy quantization, potential barriers, reflection and transmission coefficients, tunnelling, one dimensional simple harmonic oscillator, symmetric potentials and parity.
- Operator formalism and the basic postulates of quantum mechanics:
- Linear Hermitian operators and observables, eigenvalues and eigenfunctions, expectation values, rate of change of expectation values, degeneracy, simultaneous observability and commutation, the uncertainty principle. The basic postulates of quantum mechanics.

Application of Schrödinger equation to three dimensional problems:

- Free particle and particle confined to a box, Schrödinger equation in spherical polar coordinates and solving central field problems, Spherical Harmonics, orbital and magnetic quantum numbers.

Operators in quantum mechanics:

- The ladder operators in thelinear harmonic oscillator problem and the angular momentum.Introduction of spin as an intrinsic property of particles.

Schrödinger equation for two particle systems:

- The energy of arigid rotator, the deuteron; The energy, the energy level diagram and the wavefunctions of one-electron atoms.

Transformation of Representations in quantum mechanics:

- Matrix representation of wave functions and operators. Matrix representation of angular momentum operators, eigenvalues and eigenvectors of matrices, Pauli spin matrices.

Total Angular momentum and addition of angular momenta:

- The vector model, spectroscopic notation, magnetic dipole moment of an electron in an atom due to its orbital and spin angular momenta, Force experienced by an electron in an atom in the presence of an external magnetic field.

Identical particles:

- The particle exchange operator, The effect of indistinguishability of atomic particles on quantum formalism, Pauli exclusion principle.

**Evaluation:**

Two to three in-course assessment tests | 30% |

End of course written examination of three hours duration | 70% |

(Expected to answer four out of five questions) |

(45 hours of lectures and tutorials)

Objectives :

- To provide broad knowledge in electronics by developing an understanding of basic concepts in analogue and digital electronics.
- To understand the working principles of elements of digital computers.

**Syllabus :**

**Single stage transistor amplifier:**

- Analysis of different types of amplifiers with transistor models (h- and p- parameters) at wide range of frequencies.

Multistage transistor amplifier:

- Analysis of multistage transistor amplifiers with transistor models (h- and p- parameters) at wide range of frequencies.

Feedback circuits:

- Negative feedback circuits: voltage series, voltage shunt, current series and current shunt feedback amplifiers,Positive feedback circuits: Wein’s bridge, LC, quartz crystal, Hartley oscillators, Colpitt’s, Clapp and RC phase shift oscillators and Multivibrators: bi-stable, monostable and astablemultivibrators.

Analogue computing:

- Main characteristics of operational amplifiers, inverting and non-inverting amplifiers, voltage follower, current source, voltage source, filter, analogue computing circuits to perform addition, subtraction, differentiation, integration, exponentiation and logarithms, Schmitt trigger, function generator, analogue to digital converter, digital to analogue converter.

Digital electronics:

- Logic gates, Boolean functions and operations, laws and rules of Boolean algebra, De Morgan’s theorem, Boolean expressions and truth tables, Karnaugh maps, Combinational circuits
**:**adders, substractors, comparators, decoder, encoder, multiplexer, demultiplexer, Parity generator / checker, Sequential Circuits: flip-flop circuits, registers, counters and 555-timer chip.

Elements of digital computing:

- Central Processing Unit (CPU), The memory: Read Only Memory (ROM), Programmable ROMs (PROMs and EPROMs), Read / Write Random Access Memories (RAMs).

**Evaluation:**

Two to three in-course assessment tests | 30% |

End of course written examination of three hours duration | 70% |

(Expected to answer four out of five questions) |

(45 hours of lectures and tutorials)

Objectives :

- To develop an understanding of the role played by the probability distribution function for a system in its allowed microstates and of the interpretation of entropy in terms of the information related to this probability distribution.
- To develop an understanding of the Boltzmann equation for the equilibrium probability distribution as given in terms of the microstates quantities, such as the energies, particle numbers.
- To develop an understanding of the microcanonical, canonical and grand canonical formalism and relate equilibrium thermodynamic quantities to some key statistical physics parameters.
- To develop an understanding of the behaviour of important physical system by the application of equilibrium statistical mechanics.
- To apply statistical mechanics to explain simple physical phenomena such as phase equilibrium and chemical reactions.

Syllabus :

**Introduction**:

- Elementary statistics, Binomial, Gaussian and Poisson distributions.
- Basic postulates, quantum states and energy levels, micro states and macro states.

**Isolated systems**:

- Thermodynamic probability, statistical definition of temperature and entropy, the micro canonical distribution.

Closed system in contact with a heat bath:

- Boltzmann distribution and canonical partition function, applications to paramagnetic system, perfect gas, the Maxwell-Boltzmann velocity distribution, theorem of equipartition of energy.

System with variable number of particles:

- Chemical potential µ, the grand canonical distribution and the grand partition function.
- Quantum systems of non interacting identical particles, occupation number representation. Fermi - Dirac and Bose - Einstein statistics, application to black body radiation, specific heat capacity of electrons at low temperature, thermal emission of electrons, Bose-Einstein condensation.Region of validity of classical approximation.

The perfect gas in the Boltzmann limit:

- Monatomic and diatomic gases, ortho and para hydrogen.Thermodynamic equations for single phase one component systems, the Gibbs-Duhem relation, chemical reactions and the law of mass action.

**Evaluation:**

Two to three in-course assessment tests | 30% |

End of course written examination of three hours duration | 70% |

(Expected to answer four out of five questions) |