The Nature of Wavefunctions

The wavefunction describes the position of a wave in three-dimensional space at coordinates r at time t. For waves, this describes all their observable properties. Due to their wave-like nature, it was postulated in the 1920s that matter such as electrons and molecules could be described with wavefunctions also. These wavefunctions contain all the observable information about the system. Therefore, producing the wavefunctions for electrons, and for atoms and molecules as a whole, is of paramount importance for understanding the nature of chemical structure and reactivity. 

Given the importance of wavefunctions, it is worthwhile to consider some of their properties. First of all, the probability (P) of the amplitude of a wave being a particular value at a certain coordinate r and time f is given by the square of the wavefunction evaluated at position r and time t [P = ii/ r,ty]. With respect to the wave-like nature of an electron, the exact same expression holds, giving the probability of finding an electron at a particular position at a particular time. 

---