The Schrödinger equation, wave function collapse, and the time evolution of quantum states.
Introduction to Quantum Mechanics: Definition of quantum mechanics, basic principles, and the differences between classical mechanics and quantum mechanics.
Wave Mechanics: The unique mathematical framework used in quantum mechanics to describe the wave-like behavior of particles.
Postulates of Quantum Mechanics: The set of rules that govern the behavior of particles and wave functions in quantum mechanics, including the Schrödinger equation.
Bound States and Potential Wells: The properties of particles when they are confined to certain regions of space, and the role of potential wells in this confinement.
Time-Independent Schrödinger Equation: A fundamental equation in quantum mechanics that describes the time-independent behavior of particles in various potentials.
Time-Dependent Schrödinger Equation: An equation used in quantum mechanics to study dynamic quantum systems as a function of time.
Quantization of Energy: The concept of energy quantization in quantum mechanics and how it leads to the existence of discrete energy levels.
Hydrogen Atom: Understanding the Schrödinger equation for the hydrogen atom and its solutions, including wave functions, energy levels, and angular momentum.
Applications of Schrödinger Equation: From molecular physics to nanotechnology, how the Schrödinger equation is used to model many systems in the world around us.
Interpretations of Quantum Mechanics: Various interpretations of quantum mechanics, including philosophical and experimental interpretations, and the implications of each for our understanding of the natural world.
Schrödinger's Cat: The famous thought experiment designed to illustrate the strange consequences of quantum mechanics and the concept of superposition of states.
Quantum Entanglement: The phenomenon in which the properties of two particles become entangled, leading to strange effects even at large distances.
Quantum Computing: The exploitation of quantum mechanics phenomena, such as superposition and entanglement, to perform certain tasks faster or more efficiently than classical computers.
The Uncertainty Principle: One of the most fundamental principles of quantum mechanics, stating that it is impossible to know certain pairs of physical quantities with absolute precision.
Feynman Path Integrals: An alternative formulation of quantum mechanics that describes the probabilistic nature of quantum events by looking at all possible paths particles can take between two points.
Quantum Field Theory: A theoretical framework that combines quantum mechanics with special relativity to describe the interactions of particles and fields.
Time-Independent Schrödinger Equation: This is the most commonly used equation in quantum mechanics, used to study stationary states of a system. It predicts the probability distribution of particles, given their energy and potential energy.
Time-Dependent Schrödinger Equation: This equation describes the time evolution of a quantum system. It predicts how the wave function of a particle changes as it moves through space and time.
Nonlinear Schrödinger Equation: This equation describes the behavior of certain physical systems, such as Bose-Einstein condensates, that exhibit wave-like behavior. It takes into account nonlinear interactions between particles.
Klein-Gordon Equation: This equation describes the behavior of spinless particles, such as models of mesons, in the relativistic context. It is used in the study of quantum field theory.
Dirac Equation: This equation describes the behavior of particles with spin, such as electrons. It combines quantum mechanics and relativity, and successfully predicts the existence of antimatter.
Pauli Equation: This equation describes the behavior of spin-1/2 particles, such as electrons in a magnetic field. It takes into account the spin-orbit coupling, which describes the interaction between the electron's spin and its motion.
Schrödinger-Poisson equation: This equation is used to model the behavior of charged particles in an electrostatic potential. It takes into account both the wave-like behavior of the particles and the classical behavior of the electrostatic potential.