Physical Significance of Wave Function

In the physical sense, y gives the amplitude of the wave associated with the electron. It is known that in case of light waves, the square of the amplitude of the wave at a point is proportional to the intensity of light. Extending the same concept to electron wave motion, the square of the wave function, y² may be taken as intensity of electron at any point. In other words, y² determines the probability of finding the moving electron in a given region or it gives the probability density. Thus, y² has been called the probability density and y the probability amplitude. Thus, the solutions of Schrodinger wave equation replace the discrete energy levels or orbits proposed by Bohr and led to the concept of most probable regions in space in terms of y². A large value of y² means a high probability of finding the electron at that place and a small value of y² means low probability. If y² is almost zero at a particular point, it means that the probability of finding the electron at that point is negligible. Therefore, the wave mechanics approach gives meaningful wave functions, which describe the position and energy levels of electrons in an atom.