Born Oppenheimer Approximation Based on atmic nuclei and electrons ------solid state physics

The Approximation based on assumption which lead to some now known facts..

This is the approximation we can relate through the perspective of atomic nuclei and electrons. At first , in the mind of physicist ; comes the force of binding that binds two or more atoms in such a way thta total energy is less than the sum of energy constituents .

H1 + H1 = H2

With the example of Hydrogen atoms , i am fulfilling the prophecy of above paragraph and giving the concept of Binding energy that holds the atoms togather.

Binding energy equation B.E = Δmc2

We are know moving to the description of Born Oppenheimer approximation In which we will discuss molecular dynamics of molecules.

In this diagram you clearly seeing that UV light is striking the molecule and producing

electronic spectra . This will make the molecule vibrate. The changes due to this phenomenon occur will change Ev vibrational energy , ER rotational energy and EE electronic energy. All these are dependent and are quantized .It also has quantity which is not quantized and independent .This quantity is ET translational energy. It will written as in the expression of total energy as

E = EV + Er + ET + EE

Before moving further i wanted you to revise the comcept of same charges repel each other while opposite charges in nature attract each other. See the diagram for more understanding.

From now we can relate mass and velocity of atomic nucleus and electrons with the help of an example of sodium its electronic configuration is

It has been found that Mass of Nuclues is 2000 times more than the mase of electrons.

We have the general meaning from now what we can expect while relating electrons and nucleus velocities and their masses . Further we can find Hamiltonion Operation for electron and Nucleus too . The schordinger wave equation for electrons and nuclecus calculations will be the part of our next discussion.

Hamiltonion result for nucleus and electrons

Hamiltonion equation is H=T+V

By expanding he values of T and V for nucleus and electrons we get