In quantum mechanics, the dynamics of a particle in a spherically symmetric potential has a Hamiltonian of the following form:
where denotes the mass of the particle in the potential.
In its quantum mechanical formulation, it amounts to solving the Schrödinger equation with the potential V(r) which depend only on r, the modulus of r. Due to the spherical symmetry of the system it is useful to use spherical coordinates r, and . When this is done, the time-independent Schrödinger equation for the system is separable.
Read more about Particle In A Spherically Symmetric Potential: Structure of The Eigenfunctions, Derivation of The Radial Equation, Solutions For Potentials of Interest
Famous quotes containing the words particle in, particle and/or potential:
“The way to learn German, is, to read the same dozen pages over and over a hundred times, till you know every word and particle in them, and can pronounce and repeat them by heart.”
—Ralph Waldo Emerson (1803–1882)
“You don’t hold any mystery for me, darling, do you mind? There isn’t a particle of you that I don’t know, remember, and want.”
—Noël Coward (1899–1973)
“Most days I feel like an acrobat high above a crowd out of which my own parents, my in-laws, potential employers, phantoms of “other women who do it” and a thousand faceless eyes stare up.”
—Anonymous Mother. Ourselves and Our Children, by Boston Women’s Health Book Collective, ch. 2 (1978)