Particle in a spherically symmetric potential
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A particle in a spherically symmetric potential is a quantum system whose potential energy depends only on the distance from a central point and not on direction. Examples include idealised atoms, central-force systems, spherical wells, and isotropic oscillators.
Because the Hamiltonian is unchanged by rotation, its energy eigenstates can also be classified by angular momentum. The wavefunction separates into a radial part and an angular part described by spherical harmonics.
The angular solutions are labelled by the quantum numbers ℓ and m. The radial Schrödinger equation contains the original central potential together with an effective centrifugal-barrier term proportional to ℓ(ℓ+1)/r².
Different choices of the radial potential produce different spectra and wavefunctions. The method is fundamental to atomic physics because the hydrogen atom and many approximate models of nuclei, molecules, and particles use spherical symmetry to simplify a three-dimensional problem.
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- Source / publisher: Wikipedia
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- Credits: Wikipedia
- URL: https://en.wikipedia.org/wiki/Particle_in_a_spherically_symmetric_potential