# Quantum tunnel splitting

1. Aug 17, 2012

Hi,

I am was reading about a double well potential. I came across the word "quantum tunnel splitting". Can anyone tell me what this is?

For example if we have a double well potential we can have a |L> and |R> as two states. The article said that if we ignore the tunneling the two states are degenerate. But if we include the tunneling the "ground state" is split.

I do not understand why and how this is happening. Can anybody please explain me?

2. Aug 17, 2012

### Bill_K

mundhada, As you say, if we have two wells that are completely separated (no interaction between them) then the ground state with energy E will be twofold degenerate, corresponding to the fact that the particle can be located in either well. If we allow tunneling, this can be regarded as adding a small term ε to the Hamiltonian connecting the two states. The Hamiltonian is then of the form
$$\left(\begin{array}{cc}E&ε\\ε&E\end{array}\right)$$
The two eigenstates of this Hamiltonian have energy E ± ε and are no longer degenerate.