LeonhardEuler
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Hello, I'm studying P-chem and I'm having a hard time with a concept. In quantum mechanics the momentum operator is [itex]\hat{P_x}=-i\hbar\frac{\partial}{\partial x}[/itex]. The trouble I have is seeing how this reduces to the classical concept of momentum. I tried to follow the reasoning that leads to this operator back as far as I could, and what I found was that the idea was somewhat based on or inspired by the DeBroglie equation [itex]\lambda=\frac{h}{p}[/itex]. This equation implies that if the momentum of a particle is zero, then its wavelength is infinite. According to the classical concept of momentum, this would apply to any body at rest. I think the difficulty with applying this equation to a body at rest is that it is in fact made up of many particles which are not at rest and therefore do not have infinite wavelengths. So you would add thier momentums to get the toal momentum and this would imply that the wavelength is not infinite (if it even makes sense to talk about the wavelength of a group of particles). The kinetic energy operator is kind of based on the momentum operator (or the other way around) so it also does not make much sense to me. What I am looking for is an explaination of how it is that momentum and kinetic energy increase when an object starts to move according to quantum mechnaics, and also a clarification of the meaning of the DeBroglie equation. Thanks you all in advance for your replies!