The Schrodinger's wave mechanical model describes the electron as a three dimensional wave in the electronic field of positively charged nucleus. He derieved an equation which describes wave motion of an electron.

 

In the Schrodinger differential equation:

x, y, z - Cartesian co-ordinates of the electron.

m - Mass of electron

E - Total energy of the electron

V - Potential energy of the electron

h - Planck's constant

 - Wave function of the electron ....

 

The wave function may be regarded as the amplitude function expressed in terms of co-ordinates x, y, and z. The wave function may have positive or negative values depending upon the values of co-ordinates.

 

The main aim of Schrodinger equation is to give a solution for the probability approach. When the equation is solved, it is observed that for some regions of space the value of  is positive and for other regions the value of V is negative.

 

But the probability must be always positive and cannot be negative. It is, thus, proper to use ² in favour of .

 

² is a probability factor. It describes the probability of finding an electron within a small space. The space in which there is maximum probability of finding an electron is termed as orbital.

 

The solution of the wave equation is beyond the scope of JEE syllabus. The important point of the solution of this equation is that it provides a set of numbers, called Quantum numbers, which describes energies of the electrons in atoms, information about the shapes and orientations of the most probable distribution of electrons around the nucleus ....

 

Hope you understood it ......

(Well I've not written this but copied from some book ...... )