What is the significance of the de Broglie wavelength?

Question

I have just learnt quantum physics in school and learnt the concept of wave-particle duality.

But I still have trouble understanding what the de Broglie wavelength is. What does it mean for a particle to have wavelike properties? If everything is a wave then why don't we just phase through one another?

There's also a question asking you to calculate the de Broglie wavelength of the moon around earth and an electron around an atom and asking you why you can consider the moon as a "particle" but not the electron. I don't really get the answer of "wavelength significantly smaller than the orbital radius, therefore moon is a particle vice versa" though :( Why is it that wavelength being significantly smaller than the radius mean that it is a particle?

Answer 1

According to wave particle duality everything is both wave and particle simultaneously.you can't be only particle and only wave at one time that's why we don't change phase through one another. although our de broglie wavelength is a way much shorter as per formula.

λ = h/mv, in this equation since our mass is much more than that of electron; our wavelength is not bigger and even smaller than electron. hence it can't be detected by our daily life observation it requires instruments to test it.

Wavelength of moon will be significantly smaller than its orbital radius which you can calculate from formula given above. it doesn't mean it's particle, it means it will show more particle properties.when an electron is moving around nucleus its wavelength is more than its orbital radius would mean it will show more wavelike properties.

When an object shows wavelike properties it would mean electron will have a probability cloud in bigger region as shown by schrodinger equation and moon's probability cloud will be in a smaller region. smaller the probability cloud will mean more possibility to find an object in a smaller definite region which is characteristic property of a definite particle.( definite in the case of classical mechanics). you said you just started the course, you will read these things in more expanded way when schrodinger equation part will come.

Answer 2

I have not written the standard language used in textbook its about intution.

But I still have trouble understanding what is de Broglies wavelength

De Broglie postulated that associated to a matter particle with momentum p there is a plane wave of wavelength λ given by λ= h / p

What does it mean for a particle to have wavelike properties?

Its not like that something is either wave or particle. Its like when you wanted to see its wave character in experiments you will find behaving it like waves.(like do interference with electron). There is a formula for interference, you know that and in place of wavelength, you can put h/p and you will get your calculations consistent with results. Now Place a detector , you will get particle character. (Its weird!).But true

But why its showed the particle character now? Because by placing detector you wanted to find which particle passed through which hole in an interference experiment . So you wanted to see its particle character , show it showed you.

In a wave there is no notion that this wave passed through this hole or like this

Don't confuse it with trivial intution of wave. its far more than that, far different than that. But, anyway question is not about this.

Why is it that wavelength being significantly smaller than the radius mean that it is a particle?

Drop a stone in Water! or Make Wave from rope! Its energy as a whole is spread all over the wave (say in water). now start contracting all the energy (just energy not particle), and condensse the energy in a very miniscule water droplet (in a way we are reducing the wavelength) now that water drop will cross the water like a bullet. now you see its became a particle.

So Thats the the effect of increasing or decreasing wavelength. In layman terms wave is a spread like structure, and when you are condensing its parameter or properties at a point it becomes particles. ( at least classically). basically Here you are shortening the wavelength.

You precisely know the energy,position momentum all in one place in that droplet.(don't bring Heisenberg ).And that's a particle.