Neetu S.

We have to construct the wave function for a system of identical particles so that it reflects the requirement that the particles are indistinguishable from each other. Mathematically, this means interchanging the particles occupying any pair of states should not change the probability density of the system. This simple statement has the enormous consequence of dividing all particles in nature into one of two classes. An example for two non-interacting identical particles will illustrate the point. The probability density of the the two particle wave function $\Psi(\bf {r}_1, \bf {r}_2)$ must be identical to that of the the wave function $\Psi(\bf {r}_2, \bf {r}_1)$ where the particles have been interchanged. \vert\Psi({\bf r}_1, {\bf r}_2)\vert^2 = \vert\Psi({\bf r}_2, {\bf r}_1)\vert^2 We can achieve this in two ways {Symmetric case : \ \ \ }\Psi({\bf r}_1, {\bf r}_2) = \Psi({\bf r}_2, {\bf r}_1) or {Anti-symmetric case : \ \ \ }\Psi({\bf r}_1, {\bf r}_2) = -\Psi({\bf r}_2, {\bf r}_1)