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Quantum mechanical property
Quantum orbital motion involves the quantum mechanical motion of rigid particles (such as electrons) about some other mass, or about themselves. In classical
Orbital_motion_(quantum)
Function describing an electron in an atom
m_{s}} . The simple names s orbital, p orbital, d orbital, and f orbital refer to orbitals with angular momentum quantum number ℓ = 0, 1, 2, and 3 respectively
Atomic_orbital
Notation for conserved quantities in physics and chemistry
present in an orbital. For example, for p orbitals, ℓ = 1 and thus the amount of angular nodes in a p orbital is 1. The magnetic quantum number describes
Quantum_number
Branch of physics seeking to explain chaotic dynamical systems in terms of quantum theory
shares the same constants of motion for both classical and quantum dynamics. Quantum systems can also have additional quantum numbers corresponding to discrete
Quantum_chaos
Number assigned to each electron shell in an atom
electron. The principal quantum number n represents the relative overall energy of each orbital. The energy level of each orbital increases as its distance
Principal_quantum_number
Chemistry based on quantum physics
from two s-orbitals, an s-orbital and a p-orbital, or two p-orbitals. A pi (π) bond is formed from a side-to-side overlap of two p-orbitals. The pi bond
Quantum_chemistry
Laws in physics about force and motion
Newton's laws of motion are three physical laws that describe the relationship between the motion of an object and the forces acting on it. These laws
Newton's_laws_of_motion
Predecessor to modern quantum mechanics (1900–1925)
constant was often called the quantum of action. In order for the old quantum condition to make sense, the classical motion must be separable, meaning that
Old_quantum_theory
dumbbell. The other orbitals have more complicated shapes (see atomic orbital), and are denoted by the letters d, f, g, etc. The third quantum number, the magnetic
History_of_quantum_mechanics
Change in the position of an object
system in space. For example, one can talk about the motion of a wave or the motion of a quantum particle, where the configuration consists of the probabilities
Motion
Motion of charged particles
scientific and engineering uses of cyclotron motion. In quantum mechanical systems, the energies of cyclotron orbits are quantized into discrete Landau levels
Cyclotron_motion
Conserved physical quantity; rotational analogue of linear momentum
center of mass, while the orbital angular momentum is the angular momentum about a chosen center of rotation. The Earth has an orbital angular momentum by nature
Angular_momentum
Mode of arrangement of electrons in different shells of an atom
integer that precedes each orbital letter (e.g. helium's electron configuration is 1s2, therefore n = 1, and the orbital contains two electrons). An
Electron_configuration
Coupling in quantum physics
The same happens with orbital angular momenta ℓi, forming a total orbital angular momentum L. The interaction between the quantum numbers L and S is called
Angular_momentum_coupling
Attraction of masses and energy
law, relating to planetary orbital periods, would prove the inverse square law if the orbits were circles. However the orbits were known to be ellipses
Gravity
Motion problem in classical mechanics
two-body problem is used to calculate and predict the motion of two massive bodies that are orbiting each other in space. The problem assumes that the two
Two-body_problem
Quantum number parameterizing spin and angular momentum
quantum numbers s {\displaystyle s} and m s {\displaystyle m_{s}} are the spin angular momentum analogs of the two orbital angular momentum quantum numbers
Spin_quantum_number
Intrinsic quantum property of particles
This is equivalent to the quantum-mechanical interpretation of momentum as phase dependence in the position, and of orbital angular momentum as phase
Spin_(physics)
Theories of quantum chemistry explained via relativistic mechanics
Relativistic quantum chemistry combines relativistic mechanics with quantum chemistry to calculate elemental properties and structure, especially for the
Relativistic quantum chemistry
Relativistic_quantum_chemistry
Quantum-mechanical version of computer memory
In quantum computing, a quantum memory is the quantum-mechanical version of ordinary computer memory. Whereas ordinary memory stores information as binary
Quantum_memory
Quantized magnetization of charged particles
In quantum mechanics, orbital magnetization, Morb, refers to the magnetization induced by orbital motion of charged particles, usually electrons in solids
Orbital_magnetization
Different states of quantum systems
anti-bonding orbitals can be signified by adding an asterisk to get σ* or π* orbitals. A non-bonding orbital in a molecule is an orbital with electrons
Energy_level
Quantum mechanical operator related to rotational symmetry
momentum diagrams (quantum mechanics) Spherical basis Tensor operator Orbital magnetization Orbital angular momentum of free electrons Orbital angular momentum
Angular_momentum_operator
Physics phenomenon
Quantum entanglement is the phenomenon in which the quantum state of each particle in a group cannot be described independently of the state of the others
Quantum_entanglement
Electromagnetic effect in physics
The quantum Hall effect (or integer quantum Hall effect) is a quantized version of the Hall effect which is observed in two-dimensional electron systems
Quantum_Hall_effect
Physics problem related to laws of motion and gravity
three-body problem is any problem in classical mechanics or quantum mechanics that models the motion of three particles. The mathematical statement of the three-body
Three-body_problem
Atomic model introduced by Niels Bohr in 1913
proposed, quantum mechanics, in which Bohr's model of electrons traveling in quantized orbits was extended into more accurate model of electron motion. The
Bohr_model
1925 physics article by Werner Heisenberg
(how position and velocity were defined) in the old quantum theory, not classical equations of motion. Mathematically, Heisenberg used two indices for his
Umdeutung_paper
Phenomenon in quantum systems
unstable classical periodic orbits. The instability of the periodic orbit is a decisive point that differentiates quantum scars from the more trivial
Quantum_scar
Relativistic interaction in quantum physics
In quantum mechanics, the spin–orbit interaction (also called spin–orbit effect or spin–orbit coupling) is a relativistic interaction of a particle's spin
Spin–orbit_interaction
Quantum mechanical phenomenon
In physics, quantum tunnelling, barrier penetration, or simply tunnelling is a quantum mechanical phenomenon in which an object such as an electron or
Quantum_tunnelling
Extension of the Bohr model
inconsistent and led to many paradoxes. The magnetic quantum number measured the tilt of the orbital plane relative to the xy plane, and it could only take
Bohr–Sommerfeld_model
Fundamental mechanical principles
principles are fundamental to physics, from classical mechanics through quantum mechanics, particle physics, and general relativity. Action principles
Action_principles
Work being continuously done without an external input of energy
Perpetual motion is the motion of bodies that continues forever in an unperturbed system. A perpetual motion machine is a hypothetical machine that can
Perpetual_motion
The timeline of quantum mechanics is a list of key events in the history of quantum mechanics, quantum field theories and quantum chemistry. The initiation
Timeline_of_quantum_mechanics
Quantum mechanical operator interchanging particle states as arguments to a function
{x}}_{1})} is the j {\displaystyle j} -th orbital, and f i ( x → ) {\displaystyle f_{i}({\vec {x}})} is a one-electron orbital acted by K ^ j {\displaystyle {\hat
Exchange_operator
Study of forces and their effect on motion
study of motion on the molecular level Langevin dynamics, a mathematical model for stochastic dynamics Orbital dynamics, the study of the motion of rockets
Dynamics_(mechanics)
Curved path of an object around a point
spacetime, with orbits following geodesics, provides a more accurate calculation and understanding of the exact mechanics of orbital motion. Historically
Orbit
Theory of gravitation as curved spacetime
{\displaystyle T} is the orbital period c {\displaystyle c} is the speed of light in a vacuum e {\displaystyle e} is the orbital eccentricity According
General_relativity
Excited atomic quantum state with high principal quantum number (n)
these two equations leads to Bohr's expression for the orbital radius in terms of the principal quantum number, n: r = n 2 ℏ 2 k e 2 m . {\displaystyle r={n^{2}\hbar
Rydberg_atom
Equations that describe the behavior of a physical system
equation. In quantum theory, the wave and field concepts both appear. In quantum mechanics the analogue of the classical equations of motion (Newton's law
Equations_of_motion
Mathematical description of quantum state
In quantum mechanics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common
Wave_function
Description of physical properties at the atomic and subatomic scale
disciplines, including quantum chemistry, quantum biology, quantum field theory, quantum technology, and quantum information science. Quantum mechanics can describe
Quantum_mechanics
Complex type of orbit
A Rosetta orbit is a complex type of orbit. In astronomy, a Rosetta orbit occurs when there is a periastron shift during each orbital cycle. A retrograde
Rosetta_orbit
number if the observable O {\displaystyle O} is a constant of motion. In other words, the quantum number is good if the corresponding observable commutes with
Good_quantum_number
Energy level of a quantum system
In quantum mechanics, an energy level is degenerate if it corresponds to two or more different measurable states of a quantum system. Conversely, two or
Degenerate_energy_levels
Projection of spin along the direction of momentum
orbital angular momentum L and a spin S. The relationship between orbital angular momentum L, the position operator r and the linear momentum (orbit part)
Helicity_(particle_physics)
Particle effect
Zitterbewegung motion is often interpreted as an artifact of using the Dirac equation in a single particle description and disappears in quantum field theory
Zitterbewegung
Atom of the element hydrogen
in the orbital motion of the electron around the nucleus. Therefore, the energy eigenstates may be classified by two angular momentum quantum numbers
Hydrogen_atom
timeline of quantum computing and communication. Erwin Schrödinger publishes a theorem setting the basis for quantum steering and the limits of quantum state
Timeline of quantum computing and communication
Timeline_of_quantum_computing_and_communication
Spin of an electron
gives rise to the orbital magnetic dipole moment. Suppose that the angular momentum for the orbital motion is L. Then the orbital magnetic dipole moment
Electron_magnetic_moment
Scientific subjects
thermodynamics and statistical mechanics; electromagnetism; relativity; quantum mechanics, atomic physics, and molecular physics; optics and acoustics;
Branches_of_physics
Science concerned with physical bodies subjected to forces or displacements
subjects have both classical and quantum divisions of study. For instance, the motion of a spacecraft, regarding its orbit and attitude (rotation), is described
Mechanics
Formulation of quantum mechanics
logically consistent formulation of quantum mechanics. Its account of quantum jumps supplanted the Bohr model's electron orbits. It did so by interpreting the
Matrix_mechanics
Scientific field of study
fields and the general theory of relativity with motion and its connection with gravitation. Both quantum theory and the theory of relativity find applications
Physics
Methods of mathematical approximation
equations of motion and wave equations), thermodynamic free energy in statistical mechanics, radiative transfer, and Hamiltonian operators in quantum mechanics
Perturbation_theory
constant. Whereas Planck focused on a quantum of energy, Nicholson's angular momentum quantum relates to orbital frequency. This new concept gave Planck
History_of_atomic_theory
Physical quantity conserved throughout a motion
mechanics, a constant of motion is a physical quantity conserved throughout the motion, imposing in effect a constraint on the motion. However, it is a mathematical
Constant_of_motion
Branch of applied mathematics
statistical mechanics, continuum mechanics, classical field theory, and quantum field theory. Moreover, they have provided multiple examples and ideas
Mathematical_physics
Quantum mechanics taking into account particles near or at the speed of light
Bordovitsyn, V.A.; Myagkii, A.N. (2004). "Spin–orbital motion and Thomas precession in the classical and quantum theories" (PDF). American Journal of Physics
Relativistic quantum mechanics
Relativistic_quantum_mechanics
Physics principle formulated by Niels Bohr
classical orbitals connect to quantum radiation. Modern sources often use the term for the idea that the behavior of systems described by quantum theory
Correspondence_principle
Point with minimum wave amplitude
In chemistry, quantum-mechanical waves, or "orbitals", are used to describe the wave-like properties of electrons. Many of these quantum waves have nodes
Node_(physics)
Computational method in Chemistry
systems with thousands of atoms using ab initio quantum-chemical wave functions. The fragment molecular orbital method (FMO) was developed by Kazuo Kitaura
Fragment_molecular_orbital
Similar behavior of quantum systems to droplets bouncing on a fluid
instead "walk" in a rectilinear motion on top of the fluid bath. Walking droplet systems have been found to mimic several quantum mechanical phenomena including
Hydrodynamic_quantum_analogs
Theory of the strong nuclear interactions
In order to realize an antisymmetric orbital S-state, it is necessary for the quark to have an additional quantum number. — B. V. Struminsky, Magnetic
Quantum_chromodynamics
Physical quantity carried in photons
wave Helmholtz equation Light Light orbital angular momentum Light spin angular momentum Optical vortices Orbital angular momentum multiplexing Polarization
Angular_momentum_of_light
Idealised system for theoretical analysis
whenever the classical equations of motion are integrable (e.g. rectangular or circular billiard tables), then the quantum-mechanical version of the billiards
Dynamical_billiards
Class of problems in classical mechanics
In classical mechanics, the central-force problem is to determine the motion of a particle in a single central potential field. A central force is a force
Classical central-force problem
Classical_central-force_problem
Vector used in astronomy
orbital equation". American Journal of Physics. 75 (4): 352–355. Bibcode:2007AmJPh..75..352D. doi:10.1119/1.2432126. Hall, Brian C. (2013), Quantum Theory
Laplace–Runge–Lenz_vector
Influence that can change motion of an object
equilibrium. In modern physics, which includes relativity and quantum mechanics, the laws governing motion are revised to rely on fundamental interactions as the
Force
Physical quantity of dimension energy × time
stationary-action principle for classical and for quantum mechanics. Newton's equations of motion for the ball can be derived from the action using the
Action_(physics)
Electron in the outer shell of an atom's energy levels
subshells. The orbitals involved can be in an inner electron shell and do not all correspond to the same electron shell or principal quantum number n in
Valence_electron
Reference frame in quantum mechanics
A quantum reference frame is a reference frame which is treated quantum theoretically. It is used to define physical quantities, such as time, position
Quantum_reference_frame
Description of large objects' physics
describes the effect of forces on the motion of macroscopic objects and bulk matter, without considering quantum effects, and often without incorporating
Classical_mechanics
Paths of particles in the Schwarzschild solution to Einstein's field equations
{\textstyle M} , e.g., for planets orbiting their star. Schwarzschild geodesics are also a good approximation to the relative motion of two bodies of arbitrary
Schwarzschild_geodesics
Idea that small causes can have large effects
not expected in pure quantum treatments; however, the sensitive dependence on initial conditions demonstrated in classical motion is included in the semiclassical
Butterfly_effect
Quantization of cyclotron orbits
In quantum mechanics, the energies of cyclotron orbits of charged particles in a uniform magnetic field are quantized to discrete values, thus known as
Landau_levels
Quantum mechanical model
The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator. Because an arbitrary smooth potential can usually
Quantum_harmonic_oscillator
Orbital elements Orbital inclination Orbital integral Orbital mechanics Orbital motion Orbital motion (quantum) Orbital node Orbital period Orbital plane
Index_of_physics_articles_(O)
Propulsion system creating motion without propellant
December 2025. Hambling, David (17 November 2023). "Controversial Quantum Space Drive In Orbital Test, Others To Follow". Forbes. Archived from the original
Reactionless_drive
Elementary particle with negative charge
electron is described by a function called an atomic orbital. Each orbital has its own set of quantum numbers such as energy, angular momentum, and projection
Electron
Enhancement of dynamical symmetry breaking
the motion of charged particles is (partially) restricted in the two space-like directions perpendicular to the magnetic field. However, this orbital motion
Magnetic_catalysis
American physical chemist (born 1966)
hydrogen tunneling and protein motion in enzyme catalysis. Her research group has also developed a nuclear-electronic orbital approach that allows scientists
Sharon_Hammes-Schiffer
Abrupt change in a quantum particle's angular momentum
{J} -\mathbf {L} } where J is the total orbital angular momentum of the whole molecule and L is the orbital angular momentum of the electrons. If internuclear
Rotational_transition
Important atomic emission spectra
Bohr model was later replaced by quantum mechanics in which the electron occupies an atomic orbital rather than an orbit, but the allowed energy levels
Hydrogen_spectral_series
Details in the emission spectrum of an atom
energy, the correction due to the spin–orbit coupling, and the Darwin term coming from the quantum fluctuating motion or zitterbewegung of the electron. These
Fine_structure
Description of a quantum-mechanical system
function of a non-relativistic quantum-mechanical system. Its discovery was a significant landmark in the development of quantum mechanics. It is named after
Schrödinger_equation
Two systems are coupled if they are interacting with each other
coupling constant. In quantum electrodynamics, this value is known as the fine-structure constant α, approximately equal to 1/137. For quantum chromodynamics
Coupling_(physics)
Electromagnetic radiation humans can see
everyday interactions with light can be understood using geometrical optics. Quantum optics is an important research area in modern physics. The main source
Light
Tabular arrangement of the chemical elements
quantum numbers. Four numbers describe an orbital in an atom completely: the principal quantum number n, the azimuthal quantum number ℓ (the orbital type)
Periodic_table
Quantum bit
electron-on-helium qubit is a quantum bit for which the orthonormal basis states |0⟩ and |1⟩ are defined by quantized motional states or alternatively the
Electron-on-helium_qubit
Unit of magnetic moment
of an electron in an atom is composed of two components. First, the orbital motion of an electron around a nucleus generates a magnetic moment by Ampère's
Bohr_magneton
Smallest unit of a chemical element
(2008). "The Quantum Atom". University of Florida. Archived from the original on 7 December 2006. Manthey, David (2001). "Atomic Orbitals". Orbital Central
Atom
Relativistic wave equation derived by Gregory Breit in 1929
interaction between the orbital magnetic moments (from the orbital motion of charge) and spin magnetic moments (also called spin–orbit interaction). The first
Breit_equation
each other. Most commonly, the term refers to mean-motion orbital resonance, in which the bodies' orbital periods are related by a ratio of small integers
Glossary_of_astronomy
Study of the 3D shapes of molecules
molecule are determined by quantum mechanics, "motion" must be defined in a quantum mechanical way. The overall (external) quantum mechanical motions translation
Molecular_geometry
Chemical reaction in which a ring is formed/broken by adding/removing a single atom
the electrons in the orbital of the small molecule are pointed directly at the π-system. In the non-linear approach, the orbital approaches at a skew
Cheletropic_reaction
Hypothetical physical concept
combined relativity and quantum mechanics and, working with other physicists, developed quantum electrodynamics that combines quantum mechanics and electromagnetism
Theory_of_everything
Theorem in quantum mechanics
due to the orbital motion) and the quantum particle statistics of collections of such particles is a consequence of the mathematics of quantum mechanics
Spin–statistics_theorem
Study of sudden qualitative behavior changes caused by small parameter changes
and coupled quantum wells. The dominant reason for the link between quantum systems and bifurcations in the classical equations of motion is that at bifurcations
Bifurcation_theory
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