# Why does a stable orbit of $H$ atom contain an integer number of de Broglie wavelengths? [duplicate]

I was trying to understand why a stable orbit of a hydrogen atom has to satisfy that the orbit length must be a multiple of de Broglie wavelength.

I have seen some related questions like This.

But the answers seemed not very clear to me. "For the system to be stable, that is, the electron shouldn't cancell itself out". I agree with "shouldn't cancel out" But I didn't understand why only an n*π would be chosen.

I've known it should be a condition for "standing wave", but a standing wave is not necessarily n*π, is it? I'd like to know in detail about why it's stable. Moreover, what if it's an ellipse orbit? Thank you all in advance!

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