Finite potential well

A region of lower potential energy bounded by finite barriers. Bound-state wavefunctions penetrate the barriers and decay outside, while their energies remain below the exterior potential.

Schrödinger equation: The quantum equation governing how a particle’s wavefunction evolves and how its allowed energies are determined. Its solutions inside and outside the well determine the bound-state energies and leakage.
Potential energy: Energy associated with an object's position or configuration in a force field. The well is defined by how potential energy varies across space.
Quantum well: A semiconductor structure that confines charge carriers in one dimension using a lower-energy layer between barriers. It is a material realization of finite-well confinement.
Square well potential: A piecewise-constant potential with a region of one energy bounded by regions of another. The finite square well is the standard exactly specified finite-barrier model.
Quantum tunneling: The passage of a quantum particle through a classically forbidden region due to its wave nature. A finite barrier permits nonzero wavefunction amplitude beyond the well.
Wavefunction: A complex-valued function whose squared magnitude gives a quantum state's position probability density. Its spatial form reveals localization and barrier penetration.
Quantum dot: A nanoscale structure that confines electrons and holes in all three spatial dimensions. Its discrete electronic states arise from confinement by finite material barriers.
Delta potential well: An idealized attractive potential concentrated at a single point and represented by a Dirac delta function. It replaces the well’s finite width and depth with a singular limiting model.
Bound state: A quantum state localized to a region, with energy below the threshold for escaping to infinity. Finite-well eigenstates are bound while their energies lie below the exterior potential.
Energy eigenvalue: An allowed energy associated with a stationary solution of a quantum system. Each bound mode of the well has a discrete energy eigenvalue.

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Potential wellBroader topic: Real confining regions have finite barriers, unlike the ideal infinite well.