## Course Detail

 Course Name Basics of Quantum Mechanics Course Code 22PHY311 Semester 6 Credits 4

### Syllabus

##### Unit 1

Learning Objectives
Learn the basic methods of linear vector spaces.
Apply those methods to solve eigenvalue problem of quantum mechanics.
Understand function of operators and the generalization to infinite dimensions.

Introduction to Quantum mechanics: Wave function, expectation values, Schrodinger equation for free particles, Bound state problems.
Linear Vector Spaces: Basics, Inner Product Spaces, Dual spaces and the Dirac Notation, Subspaces, Line-ar Operators, Matrix elements of linear operators, Active and Passive transformations, The Eigenvalue prob-lem, Functions of Operators and related concepts, Generalization to infinite dimensions

##### Unit 2

The Postulates of Quantum Mechanics and One-Dimensional Problems
Learning Objectives
Learn and understand the postulates of quantum mechanics.
Learn and understand the symmetries and conservation laws.
Understand and solve one dimensional problems.

The Postulates, Basic postulates of quantum mechanics, Observables and operators, Measurements in quan-tum mechanics, Time evolution of the system’s state, Symmetries and conservation laws. Connecting quan-tum mechanics and classical mechanics.
Properties of One-Dimensional Motion: Bound, Unbound and Mixed States, Symmetric potentials and pari-ty, free particle, Potential step, Potential barrier and Well, Infinite square well potential, Finite square well potential.

##### Unit 3

The Harmonic Oscillator
Learning Objectives
Learn and understand the ideas and concepts of harmonic oscillator.
Learn and understand the matrix representation of various operators.
Apply quantum mechanical methods to find the expectation values of various operators and general expression for uncertainty relations.

Review of the Classical Oscillator, Quantization of the Oscillator (Coordinate Basis), The Oscillator in the Energy Basis, Passage from the Energy Basis to the position Basis. Matrix Representation of Various Opera-tors, Expectation Values of Various Operators. General expression for uncertainty relations.

##### Unit 4

Angular Momentum
Learning Objectives
Understand the basic ideas and concepts of angular momentum.
Understand the quantum mechanical methods related to the angular momentum.
Apply quantum mechanical methods for the quantitative calculations related to angular momentum.

Introduction, Orbital Angular Momentum, General Formalism, Matrix Representation, Geometrical Repre-sentation, Spin Angular Momentum, Experimental Evidence, theory of Spin, Spin 1/2 and Pauli Matrices. Eigen functions of orbital angular momentum: The Eigen value Problem of L2 and Lz, Properties of the Spherical Harmonics.

##### Unit 5

Rotations and Addition of Angular Momenta
Learning Objectives
Learn the basic ideas and concepts of rotation in quantum mechanics.
Learn theanalytical methods for the addition of more than two angular momenta.
Understand the addition of more than two angular momenta and able to findrotation matrices for coupling two angular momenta, scalar, vector, and tensor operators.

Rotations in Quantum Mechanics: Infinitesimal and Finite Rotations, Properties of the Rotation Operator, Euler Rotations, Rotation Matrices.
Addition of Angular Momenta: Addition of two Angular Momenta: General formalism, Calculation of the Clebsch–Gordan Coefficients, Addition of more than two angular momenta, Coupling of Orbital and Spin Angular Momenta, Rotation matrices for coupling two angular momenta, Scalar, Vector, and Tensor Opera-tors.

### Objectives & Outcomes

Prerequisites: Knowledge of basic and advanced mathematical physics.

Course Objectives
The course emphasizes the students to familiarize the mathematical background (Hilbert space) required to understand the basic and applied quantum mechanics, postulates, standard one dimensional problems and quantum theory of angular momentum.

Course Outcomes
After completion this course student able to
CO1. Understand and familiarize the mathematical framework (Hilbert space) required for the basic and applied quantum mechanics.
CO2. Understand the basic postulate and apply them to solve standard one dimensional problems in quantum mechanics.
CO3. Understand and learn the basic properties of harmonic oscillator.
CO4. Learn the basic concepts of quantum theory of angular momentum and apply them realistic physical problems.
CO5. Understand the concepts of addition of quantum angular momentum, standard coupling schemes and apply them in solving standard physics problems.

Skills: Basic tools (Hilbert space) required for Quantum Mechanics, Standard Coupling schemes of angular momenta used for advanced topics like nuclear physics, spectroscopy, condensed matter, quantum computation etc.

CO-PO Mapping

 PO1 PO2 PO3 PO4 PO5 PSO1 PSO2 PSO3 PSO4 CO1 3 3 3 3 3 CO2 3 3 3 3 3 CO3 3 3 3 3 3 CO4 3 3 3 3 3 CO5 3 3 3 3 3

### Text Books & Reference

Text Books

1. N Zettili, Quantum Mechanics Concepts and Applications, John Wiley & Sons, 2nd Ed, 2009.
2. J J Sakurai, Modern Quantum Mechanics, Pearson, 2nd Ed, 2016.

Reference

1. S Gasiorowicsz, Quantum Physics, Wiley India, 3rd Ed, 2003.
2. L I Schiff, Quantum Mechanics, McGraw Hill Education; 4th edition (1 July 2017).
3. David Griffiths, Introduction to Quantum Mechanics, Pearson India (LPE), 2E, 2013.
4. R Shankar, Principles of Quantum Mechanics, Pearson India (LPE), 2nd Ed, 2005.

### Evaluation Pattern

CO-PO Mapping

 Assessment Internal External Semester Periodical 1 (P1) 15 Periodical 2 (P2) 15 *Continuous Assessment (CA) 20 End Semester 50

*CA – Can be Quizzes, Assignments, Projects, and Reports.

Justification for CO-PO Mapping

 Mapping Justification Affinity level CO1-CO 5 to PO1 and PSO 1 This course imparts fundamental knowledge to students and become a foundation for applied courses. Since the contents given in all five units forms a foundation to all other courses, all COs in this course exhibits strong affinity with PO1 and PSO1. 3 CO1-PO5-PO2 and PSO2 Since all COs are strongly related to fundamental concepts, this course would equip the students in analytical and critical thinking to analyze and find solutions to any scientific problems, Thus, the entire COs are strongly related to PO2 and PSO2 and will have maximum affinity level. 3 CO1-PO5 to PO3 Since Quantum mechanics is a powerful tool in microscopic scale, any new problems arises in microscopic regime needs quantum tool to solve them. In essence this course impart underlying scientific knowledge to solve complex problems and to design and develop solutions which enhance the existing scientific knowledge. Thus, PO3 has strong affinity with all COs. 3

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