QM-105 Potential Barrier: Penetration and Scattering

What happens to a ball incident on a wall ? The ball bounces back —- is reflected. What if the wall is a region of high potential —- a potential barrier, and we replace the ball by some fundamental (or microscopic) particle? Well, if the energy is less than the potential energy, then the particles will never be able to cross the potential barrier, at least not classically. What happens Quantum Mechanically, where a wave is associated with the incident particle. The wave has a larger reach, and it turns out that the particles can be seen on the other side of the barrier. How did this magic occur? Well, the same Schroedinger equation and boundary conditions which helped us understand the discrete energy values in potential well, also yield that some particles can transmit through the barrier. Which path do the particles take? We do not know. We know they were in one region, and we know that they also reached the other region. Is there any proof of this? Yes ! Alpha decay from a nucleus. What if the particles are incident with an energy greater that the height of potential barrier. Classically, this is equivalent to the ball at a height greater than the wall height. Well, QM again yields results which are different from classical picture —- namely particles will reflect back. Why? Even in optics we learnt that when a wave travels from one medium to another, characterised by difference in their speeds, then there is always some reflection. Entering a region of different potential energy changes the speed, hence the wave-vector of the associated wave function. Enjoy ! @physicswithprof ‪@PhysicsWallah‬ ‪@Sudhir.Raniwala‬