Undergrad Are fundamental particles like electrons and protons truly matter waves?

[Jianphys17]

Hi at all, I've the following question:
How the fondamental particles (electrons, protons) are seen as matter waves, what shape and size should be these waves? They are wave-packets?

 

[drvrm]

How the fundamental particles (electrons, protons) are seen as matter waves, what shape and size should be these waves? They are wave-packets?

a fundamental particle can be represented as a wave and its wavelength depends on the momentum of the particle and such conclusions were drawn from definite experiments where the particles interfered like waves. or in other situations waves acted like particles...so one will have to go to the initial descriptions and analysis of effects like electron diffraction experiments when a beam of electrons showed diffraction pattern as produced by electromagnetic waves i.e. light.

The waves and its nature can be given by the variation of its displacement/amplitude as a function of time and space and they are solution of the equation governing the state of the particle. the picture is of 'quantum nature' therefore new equations govern the relationship between its time varying characteristics.

The second part of your question talks about wave packets...which shows that you wish to prepare packets of waves...leading to possible representation of particle nature of waves.
Kindly elaborate on your question so that we may understand further.

 

[Jianphys17]

The second part of your question talks about wave packets...which shows that you wish to prepare packets of waves...leading to possible representation of particle nature of waves.
Kindly elaborate on your question so that we may understand further.

therefore the waves of matter should be represented as localized waveforms of wave packets right ?

 

[PeroK]

therefore the waves of matter should be represented as localized waveforms of wave packets right ?

A wave packet, for example, is a normalisable solution to Schroedinger equation for a free particle (of mass $m$), and can be represented by a wave function of the form:

$$\Psi(x, t) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^{+\infty} f(k) \exp[i(kx - \frac{\hbar k^2}{2m}t)] dk$$

Where $f(k)$ represents the weighting of the underlying eigenstates. Note that $\Psi(x, t)$ is a probability amplitude.

 

[Jianphys17]

A wave packet, for example, is a normalisable solution to Schroedinger equation for a free particle (of mass $m$), and can be represented by a wave function of the form:

$$\Psi(x, t) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^{+\infty} f(k) \exp[i(kx - \frac{\hbar k^2}{2m})] dk$$

Where $f(k)$ represents the weighting of the underlying eigenstates. Note that $\Psi(x, t)$ is a probability amplitude.

so , correct me if I'm wrong, the wave-function represents the state of the particle as a localized wave packet..

 

[PeroK]

so , correct me if I'm wrong, the wave-function represents the state of the particle as a localized wave packet..

It might be localised. That depends on $f(k)$.