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)
“Each particle is a microcosm, and faithfully renders the likeness of the world.”
—Ralph Waldo Emerson (1803–1882)
“Humanity has passed through a long history of one-sidedness and of a social condition that has always contained the potential of destruction, despite its creative achievements in technology. The great project of our time must be to open the other eye: to see all-sidedly and wholly, to heal and transcend the cleavage between humanity and nature that came with early wisdom.”
—Murray Bookchin (b. 1941)