Quantum Physics

Paper Code:

PHY 511

Credits:

Contact Hours:

45.00

Max. Marks:

100.00

Objective:

This course will enable the students to -

This paper aims to develop the basic knowledge of quantum mechanics and its application to various problems. It also deals with the techniques of wave mechanics like Schrödinger equation and its solution, angular momentum and spin. The student develops the understanding of quantum nature of e.m. radiations or light and wave nature associated with microscopic particles, the notion of quantum states, operators etc.

Course Outcomes (COs):

Course	Learning outcome (at course level)	Learning and teaching strategies	Assessment Strategies
Paper Code	Paper Title
PHY 511	Quantum Physics (Theory)	The students will be able to – CO122: Understand the concept of Wave mechanics and Schrodinger equation to solve problems. CO123: Knowledge of Quantum mechanics operators and Ehrenfest’s theorem to solve problems. CO123: Apply Schrödinger equation to solve problems using Boundary condition and continuity condition, Simple harmonic oscillator and Rigid rotator. . CO124: Know the basics of Angular momentum, momentum operators and and commutation relations . CO125: Understand about Non-relativistic hydrogen atom: spectrum and eigenfunctions.	Approach in teaching: Interactive Lectures, Discussion, Tutorials, Power point presentation, Problem Solving Learning activities for the students: Self learning assignments, Effective questions, Seminar presentation, Solving numericals	Class test, Semester end examinations, Quiz, Solving problems , Assignments, Presentations

Course

Learning outcome (at course level)

Learning and teaching strategies

Assessment Strategies

Paper Code

Paper Title

PHY 511

Quantum Physics

(Theory)

The students will be able to –

CO122: Understand the concept of Wave mechanics and Schrodinger equation to solve problems.

CO123: Knowledge of Quantum mechanics operators and Ehrenfest’s theorem to solve problems.

CO123: Apply Schrödinger equation to solve problems using Boundary condition and continuity condition, Simple harmonic oscillator and Rigid rotator. .

CO124: Know the basics of Angular momentum, momentum operators and and commutation relations .

CO125: Understand about Non-relativistic hydrogen atom: spectrum and eigenfunctions.

Approach in teaching:

Interactive Lectures, Discussion, Tutorials, Power point presentation, Problem Solving

Learning activities for the students:

Self learning assignments, Effective questions, Seminar presentation, Solving numericals

Class test, Semester end examinations, Quiz, Solving problems , Assignments, Presentations

9.00

Unit I:

Introduction to Wave mechanics :

Duality of radiation and matter, De broglie’s hypothesis, justification for the relation, Experimental confirmation of l = h/p (Davission and Germer experiment).

Uncertainty principle relating to position and momentum, relating to energy and time, its applications to various quantum mechanical problems such as:

(i) Non-existence of electrons in nucleus

(ii) Ground state energy of H-atom

(iii) Ground state energy of Harmonic oscillator

(iv) Natural width of spectral line

Schrodinger equation:

Wave function and its interpretation, Schrödinger time dependent and time independent one-dimensional equation, three-dimensional Schrödinger wave equation, probability current density, physical meaning of ψ, conditions to be satisfied by ψ.

9.00

Unit II:

Operator formulation in Quantum mechanics:

Operators, algebra of operators, commutative property, linear operators, Commutator operator, eigen values and eigen functions, operators for momentum, K.E., Hamiltonian, total energy and angular momentum, Fundamental postulates of Q.M.

Hermitian operators, orthonormality, degeneracy, Commutation relations, Ehrenfest’s theorem, Bohr’s principle of complementarity, principle of superposition.

9.00

Unit III:

III

Simple solutions of Schrödinger equation:

Boundary and continuity conditions on the wave function. Particle in one dimensional box, eigen function and eigen values, discrete energy levels, generalization to 3-D and degeneracy of levels

Boundary value problems:

Step potential, Penetration through rectangular barrier, calculation of reflection and transmission coefficients. Quantum mechanical tunneling. Square well potential problem, reflection and transmission coefficient and resonant scattering.

9.00

Unit IV:

Simple harmonic oscillator (1-D Case): Schrödinger equation and its solutions, eigen function, energy eigen values. Zero point energy, parity, symmetric and anti-symmetric wave functions with graphical representation.

Rigid rotator: Schrodinger equation and its solution.

9.00

Unit V:

Angular Momentum

Introduction: orbital angular momentum,Operators for its Cartesian components, commutation relations, mutual as well as with L2 ,L+ and L- operators , their interpretation as step operators, eigen values of Lz, Total angular momentum operators, commutation relations obeyed by the components of generalized momentum operator. Commutation relation of Jz with J+ and J- , J+ and J- ,commutation relation of J2 with J+ and J-.

Essential Readings: