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| potential model (physics) | |
|---|---|
| Name | Potential model (physics) |
| Field | Theoretical physics |
potential model (physics)
Potential models in physics are theoretical frameworks that describe interactions via predefined potential energy functions, used to approximate forces between particles in systems ranging from atomic physics to astrophysics. They provide tractable descriptions that connect with observational results from experiments such as those at the Large Hadron Collider, measurements in atomic clocks, and surveys by the Hubble Space Telescope. Originating in the work of researchers like Isaac Newton and Erwin Schrödinger, potential models continue to inform studies at institutions such as the CERN and the Max Planck Society.
Potential models are typically built around a scalar function V(r, t, ...) that enters equations like the Schrödinger equation, the Hamiltonian, and the Lagrangian. The canonical quantum formulation uses H = T + V, where T is kinetic energy and V is the potential; this appears in treatments by Paul Dirac and in formalisms developed at the Institute for Advanced Study. Boundary conditions and symmetry constraints often derive from group-theoretic inputs such as Lie group representations and applications of Noether's theorem in the context of Lagrangian mechanics and Hamiltonian mechanics.
Typical potentials include the Coulomb potential used in Bohr model and atomic orbital calculations, the Harmonic oscillator potential ubiquitous in solid state physics and molecular spectroscopy, and the Yukawa potential introduced in descriptions of nuclear forces by researchers at institutions like the University of Cambridge. Other widely used forms are the Lennard-Jones potential in molecular dynamics, the Morse potential in chemical physics, and the Woods–Saxon potential in nuclear shell model studies. Effective potentials appear in Density functional theory implementations developed at the Royal Society and techniques inspired by the Hartree–Fock method.
Potential models underpin calculations of spectra in atomic spectroscopy, binding energies in nuclear physics, elastic scattering in particle physics, and structure formation in cosmology. They facilitate modeling of condensed matter phenomena studied at laboratories like Bell Labs and IBM Research, and guide experimental programs at facilities such as the SLAC National Accelerator Laboratory. In quantum chemistry and work by groups affiliated with MIT and Caltech, potentials inform reaction rates and molecular conformations, while astrophysical potentials are central to analyses by teams using the European Space Agency observatories.
Numerical solving of potential models employs methods including finite-difference, finite-element, and basis-set expansions implemented in software from research groups at Argonne National Laboratory and the Lawrence Berkeley National Laboratory. Perturbation theory as developed by Ludwig Föppl and Lev Landau and semiclassical techniques such as the WKB approximation are standard approximations. Monte Carlo methods and molecular dynamics simulations, pioneered in part at the Los Alamos National Laboratory and the Brookhaven National Laboratory, enable treatment of many-body potentials and effective interactions used in projects by the National Institute of Standards and Technology.
Validation of potential models comes from comparisons with data from experiments at the European Organization for Nuclear Research, precision spectroscopy at institutes like the National Physical Laboratory, and astrophysical observations by teams at the Space Telescope Science Institute. Limitations arise due to many-body correlations, relativistic effects treated in frameworks developed by Albert Einstein and Paul Dirac, and emergent phenomena captured by approaches such as quantum field theory and renormalization programs at the Niels Bohr Institute. Discrepancies often motivate refinements using methods from groups at the Perimeter Institute and the Kavli Institute for Theoretical Physics.
Extensions include nonlocal and momentum-dependent potentials used in modern nuclear effective field theory research, energy-dependent optical potentials applied in scattering theory, and potentials derived from lattice-based calculations carried out at centers such as the Riken and the Fermilab. Generalizations to include gauge fields and coupling to degrees of freedom are informed by work on quantum electrodynamics and quantum chromodynamics at the Keio University and Princeton University. Ongoing developments connect potential model techniques with machine-learning approaches pioneered at institutions like Google DeepMind and OpenAI for parameter estimation and model discovery.