The question is motivated by a joke-question posted in this forum, but it is serious: How would we calculate the tunneling probability for a multi-particle/multi-atom object with zero net charge?

The treatments of tunneling in the QM textbooks usually make the following implicit assumptions:

  • The object is a particle or particle-like
  • The object is charged (hence we can define the potential)

I suggest to consider the following cases:

  • Toy example: How would we calculate the probability of an atom tunneling out of a closed reservoir?
  • Realistic example: How would we calculate probability of an organic molecule tunneling through the cellular membrane?
  • Example with realistic numbers: a hydrogen atom encolosed by a metallic sphere.

I am looking for a mathematical formulation for such tunneling.



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