Energy of a particle When a particle such as an electron borrow energy to overcome a physical barrier, ( according to Heisenberg principle ) that energy has to be returned after a short while. Since total or a part of the energy borrowed has been used to overcome the barrier, how does the particle return exactly the same amount of energy? 
 A: You are confusing quantum mechanical tunneling with the heisenberg uncertainty principle.
In tunneling there is no energy expenditure. There is a probability from the boundary value solutions of the particular problem that the particle will be out of the barrier , with the same energy it had inside.


According to classical physics, a particle of energy E less than the height U0 of a barrier could not penetrate - the region inside the barrier is classically forbidden. But the wavefunction associated with a free particle must be continuous at the barrier and will show an exponential decay inside the barrier. The wavefunction must also be continuous on the far side of the barrier, so there is a finite probability that the particle will tunnel through the barrier. 

In the energy form of the Heisenberg Uncertainty Principle

one can think of loops of virtual particles within the HUP limits.
Virtual particle definition:

One may imaging a time energy square bounded by h_bar/2, but it is a mathematical space with virtual particles :

So no barrier can be overcome because there are no real particles in this image. Interactions with real particles have to conserve energy and momentum, no exceptions. In loops showing particles within the HUP there is no problem with energy conservation because nothing enters or leaves the limited by the HUP phase space in the diagrams. 
