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;
- Origin of Quantum Mechanics
- The Schrodinger Equations
- Operators, Eigenvalues and Eigenfunctions
- Solutions of Schrodinger Equations
- Quantum theory of Hydrogen Atom
- Atoms with one valence electrons
- Atoms with many electrons
Syllabus (B.Sc. Physics)
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.
Every chapter includes quizzes based on a proper understanding, single option and/or more than one preference questions, so a reader can take a look at their learning. In a few instances, PDF documents additionally supplied to you so it assists you to revise the topics. Not handiest quizzes but related experiments/simulations are also planned to included soon.
Why This Course?
- These tutorials could be useful to graduate and postgraduate students for basic ideas of quantum mechanics.
- It covers all topics as per the UGC syllabus
- A solution of pattern query paper for the pattern of question papers.
- Demonstration of the relevant experiments or simulations.
It is free, no registration fee required.
For doubt and any other problems
Weekly online interaction is possible for any doubt and problem.
NOTE: Course content is under development, so you can suggest and tell me the problems you want to include.
Formalism of Wave Mechanics
- De Broglie Equation
- Matter Waves and Wavelength
- Wave Packet| Phase & Group Velocity
- Schrodinger’s Time Independent and Time Dependent Wave Equations
- Derivation of Time Independent Schrodinger Equation in Spherical Coordinates-Hydrogen Atom
- Well behaved wave function || Normalization Constant
- Particle in a One Dimensional Box
- Symmetric and Anti symmetric Eigen functions: Degenerate states
- The Pauli’s Exclusion Principle
- Exchange Forces & The Helium Atom
- The Symmetry Character of Various Particles
- Space Quantization and Atomic Dipole Moment
- Zeeman effect-1
- Zeeman Effect Series Part-2
- Anomalous Zeeman Effect