what is the actual meaning of ? does it have any signifiacnce dealing with the structure of an atom?

it denotes the wave function of any particular  orbital in a atom

Information about a particle in a given energy level (orbit) is contained in a mathematical expression or function. This is called the wave function and is denoted by the Greek letter . The wave function is obtained by solving Schrodinger's Wave Equation. The square of the wave function () gives the probability of finding a particle (electron) within a region of space.

Acceptable solutions to the wave equation must have certain properties, and these give some insight into the significance of the wave equation.

• must be continuous


• must be finite


• must be single valued


• 

Possibly the most important outcome of all this is that we now must have a model of the atom where "probability" is important. What is the probability of finding (the) electron within a certain volume of space ?

Using Schrodingers equation we can calculate the probability density of the electron - i.e. the probability that the electron exists in a given volume of space. For example we can calculate this as a function of distance from the nucleus and we can define the "shape" of an orbital. We shall look at, for example, the radial distribution of the electron in class.

Before going onto look at where we might "place" a particular electron we need to delve a little deeper into quantum mechanics.

There are acceptable solutions to the wave equation. To obtain such solutions, it is necessary to use four quantum numbers to describe the orbital and the electron within that orbital. By defining the values of each of these four quantum numbers we can identify both the electron and the "orbit" of that electron. In some ways this is rather like giving a map reference for a person and indicating which way that person is facing. (Although these quantum numbers are not co-ordinates as such).