Free online courseQuantum physics

Course Description

The "Quantum Physics" course provides a comprehensive introduction to the fundamental principles and theories that constitute the field of quantum mechanics. With a total duration of 28 hours and 18 minutes, this course meticulously covers a broad spectrum of topics, ensuring a robust foundational understanding of quantum physics. It is classified under the Basic Studies category and falls within the subcategory of Physics.

Throughout the course, learners will delve into the intricacies of quantum mechanics, starting with the framework and definition of linearity. Initial lectures introduce crucial concepts such as Schrödinger’s equation and the necessity of complex numbers in quantum theories. The course also examines the fascinating phenomena of photons and the intrinsic loss of determinism in quantum systems, providing insights into the nature of superposition through experimental setups like the Mach-Zehnder interferometer.

As students progress, they explore more advanced topics such as the general state of a photon, spin states, and the profound concept of entanglement. The curriculum includes practical discussions on interferometers, beam splitters, and interference, culminating in the exploration of thought experiments like the Elitzur-Vaidman bomb scenario.

Other critical aspects covered in the course include the photoelectric effect, the Compton wavelength, and Compton scattering. de Broglie’s hypothesis regarding matter waves is presented, followed by an analysis of wave-packet motion, group velocity, and the wave equations for free particles. Momentum and energy operators are introduced along with their corresponding differential equations and commutators.

The course also offers in-depth discussions on the interpretation of the wavefunction, normalizable wavefunctions, and the crucial question of time evolution in quantum systems. Students are tasked with understanding the conservation of probability, Hermiticity of the Hamiltonian, and probability currents in three-dimensional spaces.

Wavepackets and Fourier representations are thoroughly elucidated, explaining concepts like widths, uncertainties, and the transformation of waves over time. The course covers the mathematical tools essential for quantum mechanics, such as Fourier transforms, delta functions, and Parseval’s identity. It also discusses expectation values of operators and their time dependencies.

Further, the course examines eigenfunctions of Hermitian operators, consistency conditions, uncertainty principles, and the mathematical rigor behind particles constrained on a circle and in potential wells. It delves into the behaviors and solutions of harmonic oscillators both differential and algebraic approaches, as well as the roles of creation and annihilation operators.

Learners are introduced to scattering states, step potentials, and the physics of high-energy wavepackets. The discussions extend to reflection and transmission coefficients, resonant transmission, and phenomena such as the Ramsauer-Townsend effect. Scattering in one-dimensional potentials, phase shifts, and Levinson’s theorem are covered in detail.

The course further includes an examination of time delay and resonance, the translation operator, central potentials, and the quantization of angular momentum. It culminates with the study of hydrogen atoms, effective potentials, and the presentation of spherical harmonics. The intricate details of energy eigenstates, degeneracies, and orbits in hydrogen atoms are thoroughly analyzed, providing learners with a holistic view of one of the simplest yet profound quantum systems.

This meticulously structured course, evaluated with an average rating of 4.16 stars, stands as an essential resource for anyone seeking to establish a strong foundation in quantum physics, paving the way for advanced study and research.