# Electron in a box model and wavefunction

In the 'electron in a box' model, is the standing wave description of the electrons same as the electron's wavefunction? If not, what is the relationship between those two? How is the wavefunction related to other concepts like De Broglie wavelength and standing wave model of an electron?

I'm so confused that I cannot generate specific questions, sorry.

• Can you elaborate a bit on what you mean by the "standing wave description of the electrons" and the "electron's wavefunction"? What is your definition for these? Nov 4, 2020 at 3:29

In the 'electron in a box' model, is the standing wave description of the electrons same as the electron's wavefunction?

A wavefunction is a solution of a quantum mechanical equation for specific boundary conditions. If your model is a solution of a quantum mechanical differential equation the solutions are wavefunctions.

How is the wavefunction related to other concepts like De Broglie wavelength and standing wave model of an electron?

In the process of defining the present quantum mechanical theory, a lot of observations were fitted to models, given names as the "De Broglie wavelength", Heisenberg uncertainty, etc. With the discovery of a strict quantum mechanical theory these are seen as projections of the correct mathematical description.

The Heisenberg uncertainty is an envelope of the mathematical demand of the commutators in the theory.

The de Broglie wavelength treats particles as matter waves, but the correct mathematically description of the particle is a probability distribution that has a wave form. Experimentally the matter wave concept is wrong, as seen in this experiment one electron at a time. The electron does not wave. The probability of interaction with the slits "waves".

The de Broglie wavelength (as well as the Bohr model) can be seen as useful tools in specific experimental situations, although the concepts are outdated theoretically .

• So... I assume that electrons (or any other "very small" matters) are neither particles nor waves although they do show certain phenomena that fit the previous conceptions of particle and wave. It sounds like wavefunctions are only mathematical tools to describe the information of them, not what they really are. So, how should these matters be called? Quantum states? Also, all the phenomena that show either wave properties or particle properties arise due to their probabilistic nature? Not because they are both wave and particle at the same time? Nov 4, 2020 at 6:38
• Also, does the interference/diffraction pattern of multiple electrons follow the electron's De Broglie wavelength? In other words, if we find the De Broglie wavelength of the electron we are shooting and input that wavelength to the double/single slit equation, will the equation output the same spacing between fringes as the spacing found experimentally (e.g. the one found from the last image you attached)? Nov 4, 2020 at 6:52
• yes to the last. The re is consistency because the de broglie wavelength was inspired by the same data, only by going one particle at a time the difference is found. Your previous questions are philosophical,at the particle level the present model is quantum mechanical, and the particles are quantum mechanical entities, seen as points at interactions and the probability of interaction carries the wave behavior. Nov 4, 2020 at 7:01
• I don't know if wavefunctions have wavelengths, but if they have or if they are assumed to exist, can the wavelength be treated as the spacing between two successive bright fringes in the probability wave pattern, which is (amplitude)^2 of the wavefunction? In one of these questions I dealt with, the mark scheme said that the de broglie wavelength of this quantum entity is the wavelength of the entity's wavefunction but it seems wrong (at least to me). Nov 5, 2020 at 12:43
• There is continuity in the physics models, for example theBohr model which is still useful because it gives similar eigenvalues and energies as the strickt quantum mechanical solution of the wave equation. The wave functions are sinusoidal so there is a wavelength. Yes, the debroglie wavelength can be the wavelength of the wave solutions , the wave functions, of the quantum mechanical equation depending on the problem, Nov 5, 2020 at 17:28