What Does Wave-Particle Duality Mean for Electrons?

[einstein1921]

I know an electron behaves like wave. I want to know what the means of this "wave"? electron wave is electromagnet wave like light or mechanical wave like sound? Thank you all!

 

[grzz]

The wave is neither electromagnetic nor mechanical. It is a wave of probability.

 

[AbsoluteZer0]

The electron has a wave function which is a probability amplitude that, when the modulus of the wave function is squared, describes the chance that an electron will take on a given quantum state. (In short, where it will be.) The precision of how well you know where it will be and when always has a degree of uncertainty as a consequence of the Heisenberg Uncertainty Principle. This principle states that you cannot know both the position and momentum of a particle without some degree of uncertainty.

The electron wave in this sense is, as grzz noted, a wave of probability (that probability being whether or not it takes on a given quantum states. In order to understand this better, take the principle of Quantum Superposition. This principle states that a given particle exists in all of its possible configurations (or possible quantum states) simultaneously, but when measured, the results of this measurement correspond to only one of those configurations.

Referring back to my first sentence, ψ is complex number. Squaring the modulus (|ψ|²) gives the probability of finding the electron in a given place at a given time.

For reference:

http://en.wikipedia.org/wiki/Wave_function
http://en.wikipedia.org/wiki/Quantum_superposition

 

[einstein1921]

The wave is neither electromagnetic nor mechanical. It is a wave of probability.

Thank you! when we explain electron interference ,we use wavefunction superpostion.as if electron is "real" wave. why can we do that?
you mean that electron actually is particle,but we use a function called wavefunction to describe the probability where it is. is my understand right?

 

[cattlecattle]

Thank you! when we explain electron interference ,we use wavefunction superpostion.as if electron is "real" wave. why can we do that?
you mean that electron actually is particle,but we use a function called wavefunction to describe the probability where it is. is my understand right?

It is a concept that has confused the greatest minds of our species at the beginning of last century, so don't get frustrated if it's not intuitive.
What you said was almost right, except in quantum mechanics, the wave function is the entire physics. Once you know the wave function, you know everything there is to know. So it doesn't make much sense to say "electron actually is a particle", it's governed by the wave function, period. Whether to call it a particle or a wave is really just a personal preference.

 

[tom.stoer]

Whether to call it a particle or a wave is really just a personal preference.

It isn't.

There are scenarios which cannot be described using a particle-like formalism; interference patterns require a wave-like description. But there are scenarios which cannot be described using this wave-like description; for example it is never the case that one actually detects one single distributed (over a region of space) electron; in a detection one always detects a point-like electron.

Therefore the electron (and all other particles) cannot be described entirely in formalism; there are aklays aspects of the other one which would be missing otherwise

 

[Naty1]

I like the last post from Tom...in the famous double slit experiment, results were surprising...as Tom notes, the photons disperse as if wavelike but when detected on the display screen appear as point [particle] like. Electrons and other matter show properties of either particles or waves.

de Broglie's prediction that matter particles share the wavelike nature of photons led to Schrödinger's wave equation describing how electron waves propagate. This wave equation can be used to predict the probability of finding an electron at some point. So when you aren't looking, an electron seems to be a wave;if you peek [detect] it's energy becomes localized and it appears as a 'particle'. Even better: when such a wave is localized [confined] as in an atom, it can have only discrete rather than continuous energy levels...leading to a limited number of allowed electron orbitals for example...and that could appear to be a tad more than just a 'probability'.

 

[haael]

But there are scenarios which cannot be described using this wave-like description; for example it is never the case that one actually detects one single distributed (over a region of space) electron; in a detection one always detects a point-like electron.

Not quite true. You can set up an array of detectors over some region of space and forget which one made the detection.

In fact the wave formalism is the full description of the quantum world. The only problem is it does not scale to the macroscopic world. We get discrete particles with probabilities instead. Why it is so is the matter of interpretation.