| 25 | | The solutions to both Poisson's and Laplace's equations satisfy the uniqueness theorem. That is, if the solution satisfies the aforementioned 2 conditions, it is the ''unique'' solution. |
| | 25 | The solutions to both Poisson's and Laplace's equations satisfy the Uniqueness theorem (see Griffith's E&M textbook). That is, if the solution satisfies the aforementioned 2 conditions, it is the solution to the equation, and further it is ''unique''. |
| | 26 | |
| | 27 | As is, the equation is set up to solve for the density (be it charge density, or matter density, etc.) given some potential (e.g. electrical or gravitational, etc.). However, in most situations we have the opposite information about a given system -- given the density, we seek the potential. This requires some numerical techniques to solving this 2nd order differential equation, especially for those systems that do not admit closed-form expressions. |
