Course Description

1. Write a short description of the course content, type of course (Theory/Theory+practice etc.)

2.Eligibility:

3. Prerequisite:

4. Duration of the course: Mention - how many hours per week, practice is to be done in campus or online.

5. Key highlights: ( like - faculty, certificate to be given from university, any job opportunity, any contact with industry person etc.)

For Diploma courses, the number 1,2 & 3 of the above will be for the whole course and number 4 and 5, will be for individual courses.

Course Objectives

• Learn methods to solve Schrodinger’s equation by WKB method, Variational method and perturbation method.
• Learn Practical application of these methods to real time problems.
  
• Learn to apply these methods to solve several problems.

Learning Outcomes

On completion of this course students will be able to

• Solve Schrodinger's equation for different systems using WKB method, Variational method and perturbation method.
• Develop Python code to solve Schrodinger's equation and find energy eigen values

Course Syllabus

Module-I

Time independent Perturbation Theory: Energy shifts and perturbed eigen states, nondegenrate and degenerate perturbation theory, spin orbit coupling

Practice 1:

• Develop  solution  for shifting and splitting of spectral lines of atoms - Stark effect.

 Module-II

Pictures of quantum mechanics: The Schrodinger picture, Heisenberg picture, the interaction picture.

Variational methods: General formalism, ground state of one-dimensional harmonic oscillator, first excited state of one-dimensional harmonic oscillator,

Practice 2: 

• Find out the energy of ground state and first excited states of  harmonic oscillator

Module-III

WKB Approximation: General formalism, validity of WKB approximation method, bound states for potential wells with no rigid walls.

Practice 3: 

• Find out the energy of particle in bound states for potential wells with one rigid wall.

Module-IV

Time dependent perturbation theory: Introduction, transition probability, transition probability for constant perturbation, transition probability for harmonic perturbation, adiabatic approximations, sudden approximations.

Practice 4:

• Calculate the transition probability rate for an excited electron that is excited by a photon from the valence band to the conduction band in a direct band-gap semiconductor by using Fermi golden rule.

Module-V

Applications of time dependent perturbation theory: Interaction of atoms with radiation, classical treatment of incident radiation, transition rates for absorption and emission of radiation,

Practice 5: (Any one)

• Light absorption and emission - mathematical formulation using electric dipole radiation
• The quantum mechanical selection rules for electric dipole transitions
• Find out expression for transition rates within the dipole approximation

Textbook:

1. Advanced Quantum Mechanics by Satyaprakash, S Chand Publications

Reference Books:

1. Quantum Mechanics: Concepts and Applications by Nouredine Zettili
2. Introduction to Quantum Mechanics, D J Griffith, Pearson, 2014.
3. Modern Quantum Mechanics, J.J. Sakurai, Pearson.

Session Plan

Session 1

Time dependent perturbation theory, energy shifts and perturbed eigen states.

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Session 2

Perturbation theory, nondegenrate and degenerate perturbation theory.

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Session 3

Spin orbit coupling.

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Session 4

Normal and anomalous Zeeman Effect - explanation, complete derivation.

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Session 5

Practice 1: (2 hours)

• Develop  theoretical solution for shifting and splitting of spectral lines of atoms - The Stark effect

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Session 6

Assessment 1:

One hour online assignment. (Mention the portion and type of assignment. If nothing is decided you can write will be declared by the faculty.)

Session 7

Perturbation theory, nondegenrate and degenerate perturbation theory.

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Session 8

Perturbation theory, nondegenrate and degenerate perturbation theory.

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Case Studies

Case Studies