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Based on my understanding, we assume that the electrons, exist as wavepackets in the solids while deriving the transport equations for transistors, we create wavepackets out of momentum eigenstates for a free particle and say this is what a classical state should look like, but why this can be the only case??

For example, cannot we have a free particle with energy on the scale of macroscopic bodies and still it is a momentum eigenstate? And why a single wavepacket, can't we have two wavepackets in opposite directions such that once i see the particle to my right and on next blink, it is magically to my left? (or will it collapse to one of the either wavepackets as soon as i see it since that constitutes a measurement?)

Is there any phenomenon that forces particles with macroscopic energy scales to exist as wavepackets in both x and k space?

Kutsit
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    Does this answer your question? Validity of naively computing the de Broglie wavelength of a macroscopic object – John Rennie Feb 20 '22 at 16:43
  • From the top answer, I get the idea that for macroscopic bodies, decoherence will do the job of destroying the phases of superposed states, but how can it affect the probability amplitudes of different states? Also, as per the wiki article there, decoherence was discovered in 1970s, then how did Shockly, Bardeen, Brittain and others developed the semiclassical approach assuming electrons to be wavepackets? Was it reverse engineered that since we always observe well defined coordinates and evolution for macroscopic bodies, they may be modelled as wavepackets? – Kutsit Feb 20 '22 at 17:02

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Is there any phenomenon that forces particles with macroscopic energy scales to exist as wavepackets in both x and k space?

In modeling nature with mathematics one has to have clear definitions.

The "wave" in a general wave equation, refers to a sinusoidal solution

The "wave" in a quantum mechanical equation that is used to model a particle is in the probability distribution, but as far as a space time identification for modeling a particle, is useless, because a plane wave solution , which is the solution with no potentials, gives an infinitesimally small probability to find the particle at a specific (x,y,z,t).

The wavepacket model allows for localized motions in fluids and sound,

Since the traveling wave solution to the wave equation is valid for any values of the wave parameters, and since any superposition of solutions is also a solution, then one can construct a wave packet solution as a sum of traveling waves

This method also can be used to form a high probability solution for finding a quantum particle at (x,y,z,t) and thus localize it.

To model a track for a free electron, one can have a wavepacket of the plane wave solutions representing the locality of the electron, a high probability of finding the electron there with that energy. This will be useful in solids , as you state.

The only "phenomenon" is that one cannot use simple plane wave solutions to represent a quantum mechanical particle, because of the identification of the wavefunction $Ψ$ with the probability (the only prediction of quantum mechanics) being $Ψ^*Ψ$.

anna v
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