Wavefunctions as a Quantity?

[Abby L 2E]

Hello.

I know we won't be tested on the particle in a box in class, but there is something in regards to the wavefunction calculation that I'd like to get cleared up. I know we can find the wavelength of any atoms with one electron, I believe? If a question asks for finding the wavelength of multiple atoms of the same element, how would calculating that work? Exactly which formula would I use for, for example, finding the wavefunction of seven carbon atoms?

Or what would be the correct way to ask this kind of question in the first place - what quantity would I be finding for an electron in a wavefunction? What exactly IS a wavefunction other than Schrodinger's equation squared and its indication of the probability of an electron in any particular space around an atom?

[Maya F 1E]

From my understanding, The de Broglie wavelength is associated with the wave-like behavior of particles and is determined by their momentum, while the wavefunction in quantum mechanics describes the quantum state of individual electrons within atoms, including their spatial distribution. When considering the electronic structure of multiple atoms of the same element, you analyze the behavior of electrons within each atom and their interactions to determine the overall electronic structure of the element.

[Abby L 2E]

From my understanding, The de Broglie wavelength is associated with the wave-like behavior of particles and is determined by their momentum, while the wavefunction in quantum mechanics describes the quantum state of individual electrons within atoms, including their spatial distribution. When considering the electronic structure of multiple atoms of the same element, you analyze the behavior of electrons within each atom and their interactions to determine the overall electronic structure of the element.

I understand that the de Broglie equation can be used to find the wavelength of particles with mass, such as the atoms of elements, and it is determined by momentum (mass times velocity). Is there a way to find the wavelength of an electron using the wavefunction? I'm not sure how to get from "behavior of electrons" and "electronic structure" (I don't know how to quantize that, or what variable it would be) to the wavelength of an electron in an atom, if that is even possible to solve for with the particle in a box equation.

What does the particle in a box equation really solve for?