Why is an object/particle Quantum Mehanical if its de Broglie particle is of the same order as its size? It is said that, if the de Broglie wavelength of a particle has approximately the same...

Why is an object/particle Quantum Mehanical if its de Broglie particle is of the same order as its size? 

It is said that, if the de Broglie wavelength of a particle has approximately the same value as its length, then it has significant quantum mechanical properties - in short, the object is know to be quantum mechanical. Is there an explanation and/or proof of this? It does seem to be common sense for a science student, but how can one come up with this rule of thumb? Thanks in advance!

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valentin68 | College Teacher | (Level 3) Associate Educator

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For an object having a certain mass, the de Broglie wave attached to it is not an electromagnetic wave (like in the case of a photon), but a probability wave (like in the case of electron). This wave have maxima and minima which shows where it is most probable and least probable to find the object positioned in space. When the length of this wave is comparable with the object linear dimensions one can say that Heisenberg principle kicks in to place. Although classical the object has a well defined position, if we take into account the de Broglie (probability) wave, the object could, or could not be there depending on its speed. This way, because the Heisenberg principle becomes to be satisfied, one can say that the object is exhibiting quantum properties.

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