- "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 scale of atoms and subatomic particles.
Wave-particle duality: The concept that particles can exhibit both wave-like and particle-like behaviors, depending on the situation.
Uncertainty principle: The principle that states that it is impossible to determine the exact position and momentum of a particle simultaneously.
Operators: Mathematical representations of physical observables, used to make predictions about a system’s behavior.
Schrödinger equation: The foundational equation of quantum mechanics, which describes how a quantum system evolves over time.
Quantum states: The wave functions that describe the probabilities of finding a particle in a specific position and/or with a specific momentum.
Superposition: The principle that states that a particle can be in a state that is a combination of two or more other possible states.
Entanglement: The phenomenon where the quantum states of two or more particles are linked in such a way that the state of one particle affects the state of the others, regardless of the distance between them.
Quantum states in three dimensions: A more advanced version of quantum states that describes particles moving in three-dimensional space.
Quantum measurements: The way in which quantum systems are observed and measured, which can have an impact on the behavior of the system.
Energy levels: The discrete energy values that a particle can occupy in a given system.
Harmonic oscillator: A physical system that oscillates around a central point, following a pattern described by the Schrödinger equation.
Hydrogen atom: An example of a quantum system that can be described using the Schrödinger equation, which is often used as a starting point for learning quantum mechanics.
Quantum tunneling: The phenomenon where particles can cross energy barriers that would be impassable in classical physics.
Dirac equation: A relativistic version of the Schrödinger equation that describes the behavior of particles moving at speeds close to the speed of light.
Quantum field theory: A more advanced version of quantum mechanics that describes particles as excitations of fields.
Quantum computing: A field that explores the use of quantum systems to perform computational tasks that are beyond the capabilities of classical computers.
- "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."