- "Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles."
The study of the behavior of matter and energy at the atomic and subatomic level. Topics may include wave-particle duality, the Schrödinger equation, and quantum mechanics in chemistry and physics.
Wave-particle duality: The idea that matter and energy can exhibit both wavelike and particle-like behavior.
Uncertainty principle: The principle that the more precisely the position of a particle is known, the less precisely its momentum can be known, and vice versa.
Superposition: The principle that a particle can exist in multiple states simultaneously until it is observed.
Entanglement: The phenomenon where two or more particles become correlated in such a way that their states depend on each other, even if separated by large distances.
Quantum tunneling: The process by which a particle can pass through a barrier that classically it would not be able to penetrate.
Schrödinger equation: The mathematical equation that describes the evolution of a quantum system over time.
Operators: Mathematical tools used to represent physical observables, such as momentum and energy, in quantum mechanics.
Eigenstates and eigenvalues: States of a system that remain unchanged when a certain operator is applied, and the corresponding values that can be measured when the system is observed.
Angular momentum: The property of a particle that determines how it rotates around an axis.
Hydrogen atom: The simplest quantum mechanical system, which consists of a single electron and a hydrogen nucleus.
Quantum numbers: Numbers used to describe the energy, angular momentum, and other properties of particles in atoms.
Atomic orbitals: Regions of space around an atom where electrons are most likely to be found.
Energy levels: The discrete levels that electrons can occupy in an atom.
Spin: A property of particles that gives rise to their magnetic properties.
The Pauli exclusion principle: The principle that no two electrons in an atom can have the same set of quantum numbers.
Quantum chemistry: It is used to study the electronic structure and properties of molecules and reactions.
Quantum mechanics of solids: It is interested in how electrons move through solids and how solids' structural properties affect their electronic properties.
Quantum mechanics of light: It involves the study of the behavior of light waves, including topics such as light-matter interaction, photon emission and absorption, and quantum optics.
Quantum field theory: It's involved in understanding the physics of subatomic particles and their interactions through descriptions using quantum mechanics and relativity.
Quantum computing: It focuses on the development of algorithms and the hardware required for quantum computation.
Quantum information theory: It studies the manipulation of quantum information, which has promising applications in cryptography, communication, and computation.
Quantum mechanics of astrophysical systems: It studies the dynamics of atoms and molecules in astrophysical systems such as stars, planets, and interstellar clouds.
- "It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science."
- "Quantum mechanics differs from classical physics in that energy, momentum, angular momentum, and other quantities of a bound system are restricted to discrete values (quantization); objects have characteristics of both particles and waves (wave-particle duality); and there are limits to how accurately the value of a physical quantity can be predicted prior to its measurement, given a complete set of initial conditions (the uncertainty principle)."
- "Quantum mechanics arose gradually from theories to explain observations that could not be reconciled with classical physics, such as Max Planck's solution in 1900 to the black-body radiation problem, and the correspondence between energy and frequency in Albert Einstein's 1905 paper, which explained the photoelectric effect."
- "These early attempts to understand microscopic phenomena, now known as the 'old quantum theory,' led to the full development of quantum mechanics in the mid-1920s by Niels Bohr, Erwin Schrödinger, Werner Heisenberg, Max Born, Paul Dirac, and others."
- "In one of them, a mathematical entity called the wave function provides information, in the form of probability amplitudes, about what measurements of a particle's energy, momentum, and other physical properties may yield."
- "Objects have characteristics of both particles and waves (wave-particle duality)."
- "Most theories in classical physics can be derived from quantum mechanics as an approximation valid at large (macroscopic) scale."
- "Max Planck's solution in 1900 to the black-body radiation problem."
- "Albert Einstein's 1905 paper, which explained the photoelectric effect."
- "There are limits to how accurately the value of a physical quantity can be predicted prior to its measurement, given a complete set of initial conditions (the uncertainty principle)."
- "Quantum mechanics is the foundation of all quantum physics."
- "Energy, momentum, angular momentum, and other quantities of a bound system are restricted to discrete values (quantization)."
- "These early attempts to understand microscopic phenomena, now known as the 'old quantum theory.'"
- "Classical physics describes many aspects of nature at an ordinary (macroscopic) scale."
- "The modern theory is formulated in various specially developed mathematical formalisms."
- "Quantum mechanics provides a description of the physical properties of nature at the scale of atoms and subatomic particles."
- "Quantum mechanics is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science."
- "The wave function provides information, in the form of probability amplitudes, about what measurements of a particle's energy, momentum, and other physical properties may yield."
- "The old quantum theory led to the full development of quantum mechanics in the mid-1920s by Niels Bohr, Erwin Schrödinger, Werner Heisenberg, Max Born, Paul Dirac, and others."