touqra said:For a spherical symmetric potential, the wavefunction can be expanded in terms of partial waves which is dependent on r and [tex] \theta [/tex]. How would this be possible, when the potential only depends on distance from source? Classically, there's no quantity, that could have depend even on [tex] \theta [/tex].
A spherical symmetric potential is a type of potential function in physics that depends only on the distance from a central point, and not on the direction of that distance. This means that the potential energy at any point in space is the same regardless of the direction in which it is measured from the central point.
An example of a system with a spherical symmetric potential is an electron orbiting a nucleus in an atom. The potential energy of the electron is determined solely by its distance from the nucleus, and not by the direction in which it is moving.
The mathematical expression for a spherical symmetric potential is V(r) = V0 / r, where V0 is a constant and r is the distance from the central point.
Some properties of a spherical symmetric potential include: it is independent of direction, it is continuous and differentiable everywhere, it approaches zero as the distance from the central point increases to infinity, and it is inversely proportional to the distance from the central point.
Spherical symmetric potentials are used in physics to model systems with spherical symmetry, such as atoms, molecules, and planets. They are also useful for solving problems involving the motion of particles in a central field, as the symmetry of the potential simplifies the calculations.