Quantum mechanics is based on a fundamental equation which is called Schrodinger equation.
Schrodinger’ s equation: For a system( such as an atom or a molecule whose energy does not change with time) the Schrödinger equation is written as:
H ψ = E ψ
When Schrödinger equation is solved for hydrogen atom, the solution gives the possible energy levels the electron can occupy and the corresponding wave function( s) of the electron associated with each energy level. Out of the possible values, only certain solutions are permitted. Each permitted solution is highly significant as it corresponds to a definite energy state. Thus, we can say that energy is quantized.
ψ gives us the amplitude of wave. The value of ψ has no physical significance. Ψ 2 gives us the region in which the probability of finding an electron is maximum. It is called probability density.
Orbital: The region of space around the nucleus where the probability offinding an electron is maximum is called an orbital.
Quantum numbers: There are a set of four quantum numbers which specify the energy, size, shape and orientation of an orbital. To specify an orbital only three quantum numbers are required while to specify an electron all four quantum numbers are required.