## Definition of the Laplace Operator

The Laplace operator, represented by $ \Delta $, is defined as the divergence of the gradient of a function.

$ {\large\Delta = \nabla\cdot\nabla = \nabla^{2} = \bigg[\frac{\partial}{\partial x_{1}},\cdots,\frac{\partial}{\partial x_{N}}\bigg]\cdot\bigg[\frac{\partial}{\partial x_{1}},\cdots,\frac{\partial}{\partial x_{N}}\bigg] = \sum\limits_{n=1}^{N}\frac{\partial^{2}}{\partial x^{2}_{n}}} $