Actually, I think it should be proportional to some symmetrized product of kronecker deltas. But how can one show that?BvU said:Not if you don't provide some more context. The way it looks now (to me) it's nonsense (##n_in_j = \delta_{ij}## ? )
First you have to show what you mean. Isn't a unit vector a constant of the integration ?PreposterousUniverse said:But how can one show that?
Solid angle is a measure of the amount of space an object takes up in three-dimensional space. It is defined as the angle formed by three intersecting planes that converge at a point. It is measured in steradians (sr).
Regular angle is a measure of the amount of rotation between two lines, while solid angle is a measure of the amount of space an object takes up in three-dimensional space. Regular angle is measured in degrees or radians, while solid angle is measured in steradians (sr).
##d\Omega## is used in solid angle integration to represent an infinitesimal element of solid angle. It is similar to using ##dx## in regular integration to represent an infinitesimal element of length. It allows for the integration of functions over a solid angle.
Solid angle is calculated by dividing the area of a spherical cap by the square of the radius of the sphere. It can also be calculated by integrating a function over a solid angle using ##d\Omega##.
Solid angle is commonly used in physics and engineering to calculate the amount of radiation or light emitted or received by a surface. It is also used in astronomy to measure the size of celestial objects and in computer graphics to simulate lighting and shading effects.