﻿ Quantum Physics | B Sc – apni Physics Physics|Science|Scholar|apniphysics.com
22 Mar 2019

15 students

# Welcome to Introductory Quantum Mechanics Course

In our daily life,  we observe the dynamics of classical objects or bodies around us. The dynamics of these objects we see as a result of externally applied force on those objects. When these objects are in motion one can find the velocity, momentum, kinetic energy and total energy associated with the object. To find all these physical variables for an object, we use Newton’s equations of motion. All such characterization of particle motion is treated under classical mechanics.

The hydrogen atom is the simplest case to explain quantum mechanics. The electron when transiting in different states absorbs and emits the radiation. This radiation explanation is helpful to understand the atomic, molecular and nuclear structures. Microscopic particles show the dual nature, provided the wavelength associated with a particle is comparable to the size of that. This is known as the de Broglie dual nature concept. There are some experiments which support the particle nature and wave nature of the macroscopic particles.

The main difference between quantum and classical mechanics if we see is of discreteness. All physical quantities that describe the quantum systems are in discrete form. You can understand it as of equal pieces which further characterized by Planck’s constant. For example, the energy of a photon (hν) where h is the Planck’s constant and ν is the frequency of radiation. So there will be 1hν, 2hν, 3hν and so on. Similarly, all other associated physical quantities like orbital and spin angular momentums are in discrete form. This form is called a quantized form.

In this course, we will cover introductory Quantum Mechanics for the B. Sc. graduate students. That includes;

1. Origin of Quantum Mechanics
2. The Schrodinger Equations
3. Operators, Eigenvalues and Eigenfunctions
4. Solutions of Schrodinger Equations
5. Quantum theory of Hydrogen Atom
6. Atoms with one valence electrons
7. Atoms with many electrons
8. X-Rays
9. Molecules

## The formalism of Wave Mechanics

Brief introduction to need and development of quantum mechanics wave-particle duality (photon as a particle, de Broglie hypothesis, particle diffraction, particle interference), wave packet, indeterminacy, complementarity.

The Schrodinger equation for a particle (free particle), operator correspondence and equation for a particle subject to forces. normalization and probability interpretation of a wave function, superposition principle, expectation value, probability current density and conservation of probability. Admissibility conditions on the wave function, Ethernet theorem.

Fundamenta postulates of wave mechanics, Eigenfunctions and eigenvalues, operator formalism, orthogonal systems, expansion of eigenfunctions, Hermitian operators, simultaneous eigenfunctions, an equation of motion

The uncertainty of position and momentum, monochromatic waves, Gaussian wave packet.

## Problems in one and Three dimensions:

Time-dependent Schrodinger equation, Application to stationary states for one dimension, potential step, potential barrier, a rectangular potential well, degeneracy orthogonality, linear harmonic oscillator

Schrodinger equation for spherically symmetric potential, spherical harmonics, hydrogen atom energy levels and eigenfunctions, degeneracy, angular momentum.

## One electron atomic spectra

Interaction with radiation, transition probability, spontaneous emission, selection rules, and lifetimes.

A spectrum of hydrogen atom, fine structure, Normal Zeeman effect, electron spin, Stern-Gerlach experiment, spin-orbit coupling (electron magnetic moment, total angular momentum) Hyperfine structure, examples of one electron systems. Anomalous Zeeman effect, Lande g-factor (Sodium D-Lines)

## Problems in one and three Dimensions:

Time-dependent Schrodinger equation, Application of stationary states for one dimension, potential step, potential barrier, a rectangular potential well, degeneracy, orthogonality, linear harmonic oscillator, Schrodinger equation for spherically symmetric potential, spherical harmonics, hydrogen atom energy levels and eigenfunctions, degeneracy, angular momentum.

## Many-Electron Atomic Spectra:

Exchange symmetry of wave functions, exclusion principle, shells, subshells in atoms, atomic spectra (Helium). LS coupling, selection rules, regularities in atomic spectra, interaction energy ideas, X-ray spectra, Mosely law, absorption spectra, Auger effect, Molecular bonding, Molecular spectra, Selection rules, Symmetric structures. Rotational, vibrational electronic levels, and spectra of molecules, magnetic resonance experiments. Raman spectra, introduction to Raman spectra.

As you know, to understand the topics of Quantum Mechanics, we also need some other physical concepts too. I called them Supporting Physical Concepts (SPCs), these concepts are the key controller to understand any difficult problem, or topic. So the learner gets familiar about any topic or that importance, this approach not only creates the interest but also involves the students in the creation of innovations.

For the course, I am upgrading the interacting videos by which you can submit your quizzes through videos and can submit at last after watching it fully. In addition to this quizzes are prepared for testing the learning in steps.

# Zeeman Effect

### Main Features

Every chapter includes quizzes based on true/false, single choice and/or multiple choice questions, so a reader can check the learning. In some cases, PDF copy also provided so it can help you to revise the topics. Not only quizzes but related experiments/simulations are also planned to incorporated soon.

• Quiz
• Notes
• Experiments

# Why This Course?

1. This course will be helpful to Graduate and postgraduate student for basic concepts.
2. Cover all major topics for all Universities/Institutes syllabus
3. Basic fundamentals along with the latest developments
4. The practice of understanding the course content in brief with Numerical Problems.
5. A solution of Sample question paper.
6. Demonstration of the related experiments or simulations and related viva questions.

### Course Fee:

It is free, no registration fee required.

### For doubt and any other problems

Weekly online interaction is possible for any doubt and problem.

### Sample Quiz

1. Heisenberg uncertainty relation holds good for

2. The energy of a particle in an infinite potential well is

3. Which of the following relation is not true according to uncertainties principle

4. The momentum of a photon is given by relation

5. The equation of motion of matter wave is given by

6. The de Broglie wavelength of a material particle depends on

### Instructor Dr Sushil Kumar

Dr. Sushil Kumar, a physicist, an eminent researcher and a teacher for the benefit of students and fellow physicists alike. Apni Physics is an effort to create a better platform and also to help the students to be able to have content at their hands whenever they want, online. Dr. Sushil continues to upload his lectures and post articles about latest researches in physics, academic, physics education, and also lessons about daily life and how physics define every aspect of our everyday movement and life.
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