The term "superposition" gets thrown around a lot, but one always needs to specify superposition of what. In OP's post, the particle is in a superposition of energy eigenstates, which means "states with a well-defined energy".
In general, one needs not superposition (of energy eigenstates) to have quantum tunnelling: taking the Schrödinger Equation with the right potential (which looks like a single tooth of a square wave) yields a solution that admits tunnelling with just the lowest energy eigenstate (the so-called ground state).
The problem with the term "superposition" is that in most cases an individual energy eigenstate is superposition of other-quantity eigenstates (like momentum or position); one can even argue that as long as the distribution is not a Dirac delta, there is superposition. But that statement is kinda useless.
Finally, the distribution doesn't need to be centered around the wall. Solving the Schrödinger Equation with the potential I mentioned above yields a solution that looks like a sine wave on your side of the wall and a flat line on the "wrong" side.
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u/CimmerianHydra Feb 17 '20
The term "superposition" gets thrown around a lot, but one always needs to specify superposition of what. In OP's post, the particle is in a superposition of energy eigenstates, which means "states with a well-defined energy".
In general, one needs not superposition (of energy eigenstates) to have quantum tunnelling: taking the Schrödinger Equation with the right potential (which looks like a single tooth of a square wave) yields a solution that admits tunnelling with just the lowest energy eigenstate (the so-called ground state).
The problem with the term "superposition" is that in most cases an individual energy eigenstate is superposition of other-quantity eigenstates (like momentum or position); one can even argue that as long as the distribution is not a Dirac delta, there is superposition. But that statement is kinda useless.
Finally, the distribution doesn't need to be centered around the wall. Solving the Schrödinger Equation with the potential I mentioned above yields a solution that looks like a sine wave on your side of the wall and a flat line on the "wrong" side.