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We know that the lower the momentum a particle has the higher will be its de Broglie wavelength, so is there any upper limit to the de Broglie wavelength of electron or any other particle due to the zero point energy of vacuum which prevents further reduction in momentum?

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Since the electron is a very light particle, when we talk about the case of zero momentum, i.e. the particle is at rest and it's position is well defined, this means that uncertainty in its momentum is infinite, so there is no case of zero momentum. (We use Compton wavelength for this case)

Further, zero point energy itself can be deducted from uncertainty principle, so we can informally say that uncertainty principle imposes upper bound for the De Broglie wavelength.

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  • $\begingroup$ Is there any theoretical value/formula for the upper limit of the de broglie wavelength? $\endgroup$ – user210956 May 15 '20 at 17:19
  • $\begingroup$ No, there is no formula for upper limit of De Broglie wavelength. For classical systems with heavier masses, the De Broglie wavelength is infinitely large and therefore macroscopic particles doesn't show wave phenomena (or impossible to detect) $\endgroup$ – Shine kk May 15 '20 at 17:26

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