Jianphys17 said:How the fundamental particles (electrons, protons) are seen as matter waves, what shape and size should be these waves? They are wave-packets?
therefore the waves of matter should be represented as localized waveforms of wave packets right ?drvrm said: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 said:therefore the waves of matter should be represented as localized waveforms of wave packets right ?
so , correct me if I'm wrong, the wave-function represents the state of the particle as a localized wave packet..PeroK said: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.
Jianphys17 said:so , correct me if I'm wrong, the wave-function represents the state of the particle as a localized wave packet..
The concept of particles as matter waves is a fundamental principle in quantum mechanics that describes how all particles, including subatomic particles like electrons and protons, can exhibit both particle-like and wave-like behavior. This means that particles can have a definite position and momentum, but also have a wavelength and can interfere with each other, similar to waves.
Particles can be described as both matter and waves because they possess both particle-like and wave-like properties. This is known as wave-particle duality. The exact behavior of a particle depends on how it is observed or measured, and it can exhibit either particle or wave behavior depending on the experimental setup.
The relationship between a particle's mass and its wavelength is described by the de Broglie wavelength equation, which states that the wavelength of a particle is inversely proportional to its momentum. This means that particles with smaller mass, such as electrons, have longer wavelengths compared to particles with larger mass, such as protons.
No, matter waves cannot be observed in everyday life because their wavelengths are extremely small and require specialized equipment to detect. However, the effects of matter waves can be seen in certain experiments, such as the double-slit experiment, which demonstrates the wave-like behavior of particles.
The concept of particles as matter waves is closely related to the uncertainty principle, which states that it is impossible to know both the position and momentum of a particle with absolute certainty. This is because the act of measuring one property of a particle affects the other property, due to the wave-like nature of particles. Thus, the more accurately we measure one property, the less accurately we can measure the other property.