## Course Detail

 Course Name Quantum Mechanics Course Code 22PHY501 Semester 7 Credits 4

### Syllabus

##### Unit 1

Three Dimensional Problems
Learning Objectives
Learn the basic methods of quantum mechanics to solve 3D potentials.
Understand the difference between various 3D potentials.
Analyze the effect of magnetic field on central potentials.

The Free Particle, The Box Potential, The Harmonic Oscillator, Central Potential, The Spherical Square Well Potential, The Isotropic Harmonic Oscillator, The Hydrogen Atom, Effect of Magnetic Fields on Central Potentials.

##### Unit 2

Approximation Methods
Learning Objectives
Understand the basic concepts of perturbation theory and approximation methods.
Learn analytical methods to solve problems of hydrogen atom like fine structure and anomalous Zeeman effect.
Apply mathematical methods for the quantitative calculations related tunnelling through a potential barrier.

Nondegenerate Perturbation Theory, Degenerate Perturbation Theory, Fine Structure and the Anomalous Zeeman Effect, The Variational Method, The Wentzel–Kramers–Brillouin (WKB) Method, Bound States for Potential Wells with No Rigid Walls, Bound States for Potential Wells with One Rigid Walls, Bound States for Potential Wells with Two Rigid Walls, Tunnelling through a Potential Barrier.

##### Unit 3

Time Dependent Perturbation Theory
Learning Objectives
Learn and understand the basic concepts and methods of time dependent perturbation theory.
Understand the basic features of the Schrödinger picture, the Heisenberg picture and the interaction picture.
Apply quantum mechanical methods to find the transition probability for a harmonic perturbation.

The Schrödinger Picture, The Heisenberg Picture, The Interaction Picture, Transition Probability, Transition Probability for a Constant Perturbation, Transition Probability for a Harmonic Perturbation, Adiabatic Approximation, Sudden Approximation.

##### Unit 4

Scattering Theory
Learning Objectives
Understand the basic ideas and concepts of scattering theory.
Understand the quantum mechanical methods related to the scattering theory.
Apply quantum mechanical methods for the quantitative calculations related to scattering.

General formalism, Connecting the Angles in the Lab and CM frames, Connecting the Lab and CM Cross Sections, Scattering Amplitude and Differential Cross Section, Scattering Amplitude, The First Born Approximation, Validity of the First Born Approximation, Partial Wave Analysis for Elastic Scattering, Partial Wave Analysis for Inelastic Scattering.

##### Unit 5

Relativistic Wave Equations
Learning Objectives
Learn the basic ideas and concepts of relativistic quantum mechanics.
Understand the basic features of relativistic wave equations.
Understand the free motion of a Dirac particle and single particle interpretation of plane (Free) Dirac wave.

The Klein-Gordon Equation, Free Spin Zero Particles, Interaction of Spin Zero Particles with Electromagnetic Field, The Dirac Equation, Free motion of a Dirac Particle, Single Particle interpretation of Plane (Free) Dirac Wave.

### Objectives & Outcomes

Pre-requites
Knowledge of mathematical physics and basic quantum mechanics.
Course Objectives
The course emphases the students to familiarize the application of quantum mechanics to single, many body problems, approximation methods and scattering theory. Students also learn the basic concepts of relativistic quantum mechanics.
Course Outcomes: After completion this course student able to
CO1. Understand different aspects of the 3 dimensional Schr ̈odinger equation and solve problems related to 3D Cartesian and spherical polar coordinates.
CO2. Learn and apply the main approximation methods for stationary states.
CO3. Learn the basic ideas and methods of time-dependent perturbation theory.
CO4. Learn and apply the scattering theory and solve problems related to scattering.
CO5. Understand and learn the concepts and methods related to relativistic quantum wave equations.
Skills: Analytical skills are developed by solving problems related to advanced topics in quantum mechanics through assignments and quizzes.

CO-PO Mapping

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

### Text Books & References

Text Books

1. N Zettili, Quantum Mechanics Concepts and Applications, John Wiley & Sons, 2nd Edition, 2009.
2. JJ Sakurai, Modern Quantum Mechanics, Cambridge University Press; 3rd Edition, 2020.
3. W Greiner, Relativistic Quantum Mechanics, Springer, 3rd Edition, 2000.

References

1. F Schwabl, Quantum Mechanics, Springer, 4th Edition, 2007.
2. L I Schiff, Quantum Mechanics, McGraw Hill Education; 4th edition, 2017.
3. David Griffiths, Darrell F. Schroeter, Introduction to Quantum Mechanics, Cambridge University Press
India Pvt Ltd, 3rd Edition, 2019.

### Evaluation Pattern

 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 and PO1 CO1 is related to understand different aspects of the 3 dimensional Schr ̈odinger equation. This improves student’s knowledge in quantum mechanics and hence the affinity level is 3. 3 CO1-PO2 Since PO2 is related to problem analysis and CO1 is also related to solve problems related to 3D Cartesian and spherical polar coordinates. Hence the affinity level between CO1 and PO2 is mentioned as 3. 3 CO2-PO1 CO2 is related to learning the main approximation methods for stationary states in quantum mechanics. Hence the affinity level is 3. 3 CO2-PO2 As CO2 is related to apply main approximation methods to stationary states. Since PO2 is related to developing analytical skills, the affinity level between them is 3. 3 CO3-PO1 Since PO1 is related to acquiring knowledge in quantum mechanics, CO3 has maximum affinity 3 when mapped with PO1. 3 CO3-PO2 CO3 is related to the applications of time dependent perturbation theory. As problems will be solved employing these methods and the analytical skills of students will be improved. Since PO2 is related to improving analytical skills, CO3 has maximum affinity to PO2 and hence given an affinity level of 3. 3 CO4-PO1 CO4 is related to learning scattering theory for quantum mechanical problems. As PO1 is related to improving knowledge of physics fundamentals, CO4 has maximum affinity of 3 with PO1. 3 CO4-PO2 CO4 is for solving problems related to scattering. Since PO2 is related to the development of analytical skills of students and maximum affinity level of 3 is given for CO4-PO2 mapping. 3 CO5-PO1 CO5 is related to understanding of basic concepts of relativistic quantum mechanics. Since PO1 is related to improving student’s knowledge in quantum mechanics, maximum affinity level of 3 is given for CO5-PO1 mapping. 3 CO5-PO2 CO5 improves the analytical skills of students. As PO2 is related to improving analytical skills, CO5 has maximum affinity with PO5 and hence given an affinity level of 3. 3 CO1-PSO1 PSO1 is related to demonstration of proficiency in quantum mechanics which essential to understand the three dimensional Schr ̈odinger equation. Hence the affinity level is 3. 3 CO1-PSO2 CO1 deals with knowledge and tools of quantum mechanics to solve 3D problems. Hence CO1 completely map with PSO2 and an affinity level of 3 is assigned. 3 CO2-PSO1 CO2 is related to understanding of the main approximation methods for stationary states which map completely with PSO1. So the affinity level is 3. 3 CO2-PSO2 Since PSO2 is related to improving knowledge in quantum mechanics. Hence the affinity level between CO2 and PSO2 is 3 instead of 2 or 1. 3 CO3-PSO1 Since CO3 is related to application of time dependent perturbation theory which require basic understanding of quantum mechanics, CO3-PSO1 mapping has the affinity level 3. 3 CO3-PSO2 The affinity level between CO3 and PSO2 is 3 since CO3 deals with applications of time dependent perturbation theory to solve problems which eventually improves not only analytical skills of students but also their knowledge in quantum mechanics. 3 CO4-PSO1 CO4 is related to learning and applying scattering theory to quantum mechanical problems. Hence CO4-PSO1 mapping has the affinity level 3. 3 CO4-PSO2 The affinity level between CO4 and PSO2 is 3 since the CO4 deals with understanding and solving problems related to scattering. 3 CO5-PSO1 CO5 is related to relativistic quantum mechanics and hence CO5-PSO1 mapping has the affinity 3. PSO1 is related to demonstrating proficiency in mathematics and mathematical concepts to understand quantum mechanics. 3 CO5-PSO2 The affinity level between CO5 and PSO2 is 3 since CO5 deals with understanding and application relativistic quantum mechanics. 3

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