

Potential Barriers
Hi. Does a particle really go through a wall or through a potential barrier, or is it possible that a) a particle hits the wall, and the energy is transferred (just like those balls on the double strings that tranfer energy to the last ball) until the other side of the wall emits it's own electron? Perhaps the tranfer of energy has identical velocity as the particle, or b) that the energy of a particle trapped inside a finite potential energy well "vibrates" the energy of the barrier so that the energy, again, is absorbed into the barrier and expelled on the outside? Analogy: Suppose there is some water behind a physical barrier, now the wave will propagate through the barrier with a decreased amplitude and appear on the other side, even though it is "impossible" for the wall to contain such a wave. What if the barrier COULD contain the wave, and the wave COULD vibrate up against the barrier so that the barrier vibrated back, which would, in turn, vibrate the water on the other side of the barrier with a decreased amplitude. Someone has to have asked this before, but I want to know how QM is so sure this doesn't happen. Please no differential equations in the answer, my math is limited to CALC III.
Jennifer Roush
Dear Jennifer, Quantum mechanics concepts especially the first ones that you learn are usually the hardest to conceptualize but they are the foundation for a totally new pair of spectacles. Classically, you worry about concepts such as the potential barrier being made up of some material and thus want to know what "process" goes on to generate the transmission through the barrier. WELL, the potential barrier is not material but is the tug of the electric force acting on the electron (in that particular case). Classically, the electron has no chance of getting around the barrier if its energy is not higher than the barrier. It just cannot. But if you view it as a quantum particle, then it is not always a particle. Sometimes it is better to think of it as a wave. Actually it is a wave function which when squared gives the probability for being at a certain place. If it is free, the wave looks like a sine and thus squaring it gives equal probability for it to be anywhere (it's free). If it remains bound between two barriers, then it can bounce around inside but cannot get out, right? Wrong. There can be some PROBABILITY for it to be underneath the barrier. When you solve the DEs, you get a sine wave where (EV) > 0 and an exponential decay where (EV) < 0. So if the barrier is very thick, there will be near zero probability for it to be near the outside and effectively it is confined. It can tunnel though if the barrier is thin. As far as your transfer of particle theory, I don't know if there is any way of testing this but perhaps it is just another way of saying the same thing. After all, your particle going against the wall must disappear and a "new" one must reappear. BUT, at some stage in QM you will learn that two particle of exactly the same type are indistinguishable. So how do you know which one was which. They might as well have been the same. It is hard to get used to, but at the quantum level, particles are not always fixed objects but can be waves. It is not just that you get an energy transfer either. If you detect the electron on the other side, you see the same charge, magnetic moment, etc. This should put a damper on your water argument. I hope this helps ! Sincerely,
Glenn Blanford, Ph.D. 
last modified 2/20/1998 physicsquestions@fnal.gov 
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