what is the meaning of hopping energy? i know some, but i like understand deeply.:shy:
You really should provide some context on where you found this phrase, since this could be a number of things. Keep in mind that the MORE you explain your question, the less we have to go back and forth to narrow down exactly what it is that you are asking.
If by "hopping energy", you mean the term normally assigned as "t" in the hopping integral such as in the tight-binding approximation, then it is really what its name says, the energy needed for the particle to hop from one location of the lattice to another.
You can't understand anything "deeply" on a public forum. The only way you can do that is through a proper study.
It's something like a kinetic energy. If you discretize the Schroedinger equation on a square lattice then you find that the hopping term [itex]\gamma=\hbar^2/(2ma^2)[/itex] where [itex]a[/itex] is the lattice constant. The hopping energy generally sets the energy scale of your system (for example the bandwidth is usually measured in terms of the hopping constant).
edit: proably it should be [itex]\gamma=\hbar^2/(ma^2)[/itex]
Separate names with a comma.