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Quantum tunnel splitting

  1. Aug 17, 2012 #1
    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. jcsd
  3. Aug 17, 2012 #2

    Bill_K

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    Science Advisor

    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
    [tex]\left(\begin{array}{cc}E&ε\\ε&E\end{array}\right)[/tex]
    The two eigenstates of this Hamiltonian have energy E ± ε and are no longer degenerate.
     
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