Question

in quantum mechanics, when we analyze the potential step: we say that a classical bowling ball do not reflect because its wavelength is so small that we do not have a step whose rising distance is comparable with the ball's wavelength.

Question: If I assume we a particle whose mass is 100m, and it is composed of 100 particles having mass m. If the big mass moves with a constant speed v then all the small particles move with the same speed, so the momentum of the 100m composition is 100 times greater than its sub particles, consequently its wavelength is 100 times smaller. If we have a potential step whose rising distance is comparable with the wavelength of the sub particles, so it is not comparable with the 100m composition particle.

Ie know that a bowling ball does not reflect, so I should consider the particles as a whole. However, I do not understand what changes for small particles when they have some friends while entering a potential step that they pass without reflecting instead of having a reflection probability -as in the case when we send a small particle.

Answer 1

You are right in the sense that an object is always considered as a whole and not as consisting of microconstituents when dealing with such aspects. And also De Broglie hypothesis that more will be the mass i.e. momentum, smaller will be the wavelength associated.

Keep one thing in mind that the problem above discussed can be dealt classically and position and momentum in such problems can be found simultaneously. But in case of small particles, small here I mean to say that their wavelength is comparable or more to that step height, then these particles must be dealt quantum mechanically. Thus instead of assuming them a particle, we will assume that to be a travelling wave whose position will be given by a probability density term.

Now all the wave like properties will be applicable here along with the assumptions that it travels in straight line, diffraction, interference etc. It will be diffracted only when the obstacle size/ step size is of the order of its wavelength.

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