I am a 12th grade student I want to clarify some fundamentals about waves.It's clear to me when some one says sound propagates As a wave(the variations of air densities as a function of distance from the source at an instant of time represent a sinusoidal function.).But what does it mean when someone says electron behaves as a wave?Does it mean it's trajectory represents a wave?
The “wave” of the electron is a probability wave used to describe quantum effects. For quantum-scale particles that have not had any effects measured (e.g. spin, momentum, position), the “particle” cannot be described as a discrete object in one spot/state, but as a wave existing in and moving through multiple states at once. This wave is described by the wavefunction, and by taking the absolute value and then squaring it, you get the probability distribution. This $|\psi|^2$ tells you where you are most likely to find the electron upon measurement.
It’s a very weird and intriguing phenomenon that has no classical analogue.
I am explaining my understanding: The wave particle effect is the momenta effect of a wave packet describing an energetic identity. So a photon is neither a wave nor a particle, it is not a wave sometimes and a particle some other times; it is a wave packet. Due to its momenta effect it may have some particle behavior, and as defining momentum in particles is mass x velocity: mass is an intrinsic property and speed is extrinsic, the momentum is a whole one intrinsic property in massless particles like photons.
Wave-particle duality only exists in quantum mechanics, not in acoustics.
In the QM realm, that duality refers to the fact that very very very small objects can either manifest themselves as particles or as waves, depending on what type of measuring device you are using on them. So for a huge number of photons traveling through a prism, they act like waves, but for single photons striking a metal surface in a vacuum, they act instead like particles.
Similarly, electrons being boiled off a hot metal object in a vacuum behave like miniature machine gun bullets, but when beamed through a single crystal of a metal like nickel they diffract just as if they were waves instead.
I am actually a 7th grade student interesting of your level... but let us get to the fundamentals in quantum mechanics when we speak of wave-function you can interpret the Doppler effect which applies to sound and general particles if someone claims an electron behaves in a wave and as a particle you can infer that both of those are correct and scientifically tenable... Furthermore lets prolong the common example of the electron it behaves as a particle on a plane not an asymptote but just a sinusoidal wave it also oscillates continually and because it is a particle you can detect the absolute in Brownian momentum with the wave, hence we can derive some fascinating properties but back to the corroboration it has been proven with the double-slit experiment in 1801 which was attempted by Thomas Young to prove the nature of light which was shown and it links to one of the most perhaps prominent theories that quickly graduated to the possible theory of the universe string theorem which describes every elementary particle from the standard model a standing wave, furthermore each wave has a specific probability to there amplitude in space in there quantum system propagation could change the magnitude in multiple ways at any given point. Thus I believe it is more than safe to say that the electron varies in the vibration of a wave given the function (I hope that helps) Also if you are interested in things like these topics perhaps you would enjoy a book I just read by Tim James titled Fundamentals on the cover it states how quantum mechanics and particle physics explains absolutely everything!