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)
“Standing on the bare ground,—my head bathed by the blithe air, and uplifted into infinite space,—all mean egotism vanishes. I become a transparent eye-ball; I am nothing; I see all; the currents of the Universal Being circulate through me; I am part and particle of God.”
—Ralph Waldo Emerson (1803–1882)
“Laughing at someone else is an excellent way of learning how to laugh at oneself; and questioning what seem to be the absurd beliefs of another group is a good way of recognizing the potential absurdity of many of one’s own cherished beliefs.”
—Gore Vidal (b. 1925)