- "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."
Quantum mechanics is the foundation of modern physics and is used in computational physics to study the behavior of subatomic particles and materials.
The wave-particle duality: This is the concept that fundamental particles often exhibit both wave-like and particle-like behaviors.
The Schrodinger equation: This equation describes how the state of a quantum system evolves over time.
Quantum states and operators: Quantum states are represented by state vectors in a Hilbert space, while operators act on these state vectors and describe observables such as position or momentum.
Quantum superposition and entanglement: Quantum superposition is the phenomenon whereby a particle can exist in two or more states simultaneously, while entanglement is the correlation between the quantum states of two or more particles.
Uncertainty principle: This principle states that it is impossible to precisely determine both the position and momentum of a particle simultaneously.
Quantum measurement and collapse of the wavefunction: When a quantum system is measured, the probability distribution of its properties collapses to a single value.
Quantum harmonic oscillator: The harmonic oscillator is a simple model that has many applications in quantum mechanics.
Hydrogen atom: The hydrogen atom is the simplest atom and serves as a key example to understand the behavior of electrons in atoms.
Time-independent perturbation theory: This technique is used to calculate the properties of a system that has been perturbed from its initial state.
Time-dependent perturbation theory: This technique is used to study changes to a quantum system over time due to a perturbation.
Scattering theory: This is the study of how particles scatter off one another and is important for understanding processes such as nuclear reactions.
Tunneling: Tunneling is the phenomenon where a particle can pass through a barrier even if its energy is less than the height of the barrier.
Relativistic quantum mechanics: This is the study of how quantum mechanics can be reconciled with relativity and is necessary for understanding the behavior of particles traveling at high speeds.
Many-particle systems: The behavior of a system of many interacting particles is crucial in fields such as condensed matter physics.
Quantum algorithms: Quantum computers use the strange properties of quantum mechanics to perform certain calculations more efficiently than classical computers.
Quantum Computing: It involves using quantum bits or qubits to process information and solve complex mathematical problems which are beyond the scope of classical computers.
Quantum Cryptography: It is the study of the security of communication through quantum means, like quantum key distribution, which enables the encoding and decoding of messages on the basis of quantum-mechanical principles.
Quantum Information Theory: It deals with the transmission and processing of information using quantum systems to achieve greater efficiency and security.
Quantum Field Theory: Describes the behavior of quantum fields, which are the fundamental entities that underlie all particles and fields in the universe, and used to describe high-energy particle interactions.
Quantum Optics: Focuses on the behavior of light and its interaction with matter at the quantum level, relevant for the design of new materials, communication systems, laser technologies, etc.
Quantum Simulation: It involves simulating the behavior of complex physical systems or chemical reactions, which are very difficult, if not impossible, to simulate on classical computers.
Quantum Control: The study of how to manipulate the dynamics of quantum systems, e.g., to minimize energy losses or to maximize the efficiency of quantum machines.
Quantum Metrology: The precision measurement of physical quantities, such as time, frequency, distance, etc., using quantum systems, is used in a wide range of applications, e.g., navigation, synchronization, and atomic clocks.
- "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."