- "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 how particles and waves interact, and how they can be described mathematically.
Wave-particle duality: The concept that matter and energy can exist as both a wave and a particle simultaneously.
Probability and statistics: The mathematical tools used to describe the behavior of quantum systems.
Schrödinger equation: A fundamental equation of quantum mechanics that describes the behavior of a quantum system.
Quantum states: A description of a quantum system that includes its energy, position, and other relevant properties.
Wavefunctions: Mathematically describing quantum states.
Orbital theory: The study of electron arrangements in atoms and molecules.
Quantum numbers: Numbers that describe the properties of an electron in an atom.
Spin: A fundamental property of all particles that leads to their magnetic behavior.
Operators: Mathematical tools used to describe quantum mechanical systems.
Eigenvalues and eigenvectors: The properties of operators that describe the states of a quantum system.
Heisenberg uncertainty principle: The principle that it is impossible to simultaneously know the precise values of certain pairs of properties of a quantum system.
Uncertainty and measurement: The role of measurement in quantum mechanics and how it affects the properties of particles.
Superposition: A principle of quantum mechanics that states that particles can exist in multiple states simultaneously.
Entanglement: A phenomenon in which the states of two particles are correlated even if they are separated by a distance.
Quantum tunneling: A phenomenon in which particles can pass through potential barriers even if they do not have sufficient energy to do so classically.
Time evolution: The behavior of quantum systems over time and the role of the Schrödinger equation.
Approximation methods: The mathematical tools used to simplify the calculation of quantum mechanical systems.
Applications of quantum mechanics: The various fields in which quantum mechanics plays a role, including chemistry, physics, and materials science.
Non-relativistic quantum mechanics: Mathematical framework that describes the behavior of non-relativistic particles such as electrons and atoms.
Relativistic quantum mechanics: Mathematical framework that incorporates relativistic effects, such as the speed of light, into the description of the behavior of particles such as electrons and atoms.
Quantum field theory: Mathematical framework that extends quantum mechanics to include the behavior of fields, such as the electromagnetic field.
Density functional theory: A theory that uses the electron density of a system to determine its energy and properties.
Quantum mechanics of solids: Mathematical framework that describes the behavior of electrons and atoms in solids, including the band structure and electronic properties of materials.
Quantum computing: The use of quantum mechanics to process and manipulate data, with applications in cryptography and computer science.
Quantum optics: The study of how light and matter interact at the quantum level, with applications in communication and sensing.
Quantum information theory: The study of quantum mechanics as it relates to the processing and transmission of information, with applications in computer science and cryptography.
Quantum thermodynamics: The application of quantum mechanics to the study of thermodynamics, including the behavior of small systems and the limits of energy conversion.
Quantum chemistry: The application of quantum mechanics to the study of chemical systems and reactions, with applications in materials science, drug design, and catalysis.
- "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."