I didn't read the entire article, but I did peruse it. He comes up with a version of the Shroedinger eqn with the stock price s taking the place of position. He has a potential function of \frac{1}{s^2}. I didn't see where he changed over to something like \frac{1}{(s - s_0)^2} so his ranges run from negative money to positive, an unusual range to say the least. What's more, the shape of the potential is wrong for tunneling since it has no 'wall' like a particle in a box would have. I didn't read what variable represents energy in this equation, but perhaps it is \frac{1}{2}m(s')^2 where m is something like the mass of the stock. If a stock has a fixed mass, there is a fixed energy to the stock which in conjunction with the potential defines the endpoints of the range. Perhaps knowing the endpoints of the range would then tell you the energy and mass of the stock. Then he calculates the transition and reflection probabilities at the ends of the range and I suppose this models the behavior of real stocks both while range bound, and when they tunnel out of their ranges.
I find some differences between this description of stock behavior and quantum tunneling. In the later case, the particle appears on the opposite side of a classically forbidden region. I don't know that stock prices have classically forbidden regions. Another is that the range in quantum tunneling is static. The range that a stock trades in is caused by sellers at the high end and buyers at the low end. The forces exerted by these buyers and sellers is time dependent. You can't tell the difference between a shift in the range, or a price that has tunneled out of an existing range. Certainly, as soon as a stock price were to tunnel out of it's range, that range would cease to have any existence, unlike say an alpha particle which has escaped a nucleus which continues to exist. The stock price s is quantized, but the position x of a particle in a box is not.
