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nashsth

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1) Is the de Broglie wave the same thing as a wavefunction of a particle? Then, would this imply that the de broglie wavelength is the wavelength of the wavefunction?

2) Would it be valid to say that if the de broglie wavelength is large (so large that it is measurable), the particle that the de broglie wavelength "belongs" to has a larger uncertainty in position and that if the de broglie wavelength is small, the particle has a smaller uncertainty in position?

Linking this with the wavefunction concept, I am thinking that if the de broglie wavelength is large, then the wavefunction is more "spread out". Similarly if the de broglie wavelength is small, the wavefunction is more "localized" and so there is a greater probability of finding a particle within a smaller range.

3) Is quantum tunneling a phenomenon where a particle literally burrows through a potential barrier? Or is it just the observation that a particle can be on the other side of the barrier not because it literally burrows through but because the wavefunction of the particle is so "delocalized"/spread out that it spans the length of the potential barrier, hence the probability of observing the particle on the other side is small but non-zero? (In short, is quantum tunneling just an application of the uncertainty principle where there is a large uncertainty in position hence it is possible to find the particle on the other side of the barrier? The de broglie relation looks somewhat similar to the uncertainty principle: λ*p = h vs Δx*Δp ≥ ħ/2 so this is why I thought that there is a connection between the de broglie wave and the wavefunction.)

These questions arose when I attempted to answer the question "can a baseball tunnel through a thin window". My thoughts were that since the de broglie wavelength of a massive object like a baseball is very tiny (beyond detectable), it would mean that the wavefunction of the baseball is highly localized. Because of this localization, the wavefunction of the baseball doesn't span the length of the window hence the probability that the baseball tunnels through the window is practically 0.

Thanks for your help! :-)

-Nash