# How can the electron be a wave? [duplicate]

This question already has an answer here:

I read about Rutherford's failed attempt to describe the atomic model. Then I read about Bohr's model and his postulates. Ok, that was fine. But then I read in my book a statement that shocked me:

One and the most important discovery of quantum mechanics was that electron behaves as wave....

Now, how can an electron, a particle revolving around the nucleus in a quantized orbit, be a wave?

## marked as duplicate by John Rennie, Kyle Kanos, ACuriousMind♦, Waffle's Crazy Peanut, DanuDec 22 '14 at 16:19

• possible duplicate: physics.stackexchange.com/q/40985 – Martin Dec 22 '14 at 9:06
• An electron doesn't behave like a wave. More importantly, an electron is not even an objects on its own. It only "exists" as part of the dynamic of a quantum field. None of the people who helped to discover and develop quantum mechanics could have known that. They were still trying to make sense of a completely new reality by using language that was well suited to describe the old models of the classical world. As a result much of the historic language is just an artifact of an incomplete discovery. One shouldn't take it too seriously. What you need is the intuition for quantum field theory. – CuriousOne Dec 22 '14 at 9:06
• in other words: There is no purely physical intuition, because intuition comes from classical physics and this is nonclassical. Still, there is no real "wave-particle-duality" in the sense always described. It's all fields and excitations of fields... – Martin Dec 22 '14 at 9:08
• youtube.com/watch?v=M4_0obIwQ_U Maybe this will help – Daz Hawley Dec 22 '14 at 9:14
• possible duplicate of Is the wave-particle duality a real duality? – John Rennie Dec 22 '14 at 11:18

If one wishes to get a clear image about what is a quantum object, it is very recommended to read the Feynman's path integral,

https://www.scribd.com/doc/227963184/Feynman-Hibbs-Quantum-Mechanics-and-Path-Integrals-pdf#scribd

The electron behaves as a wave because inside an atom, it behaves as a quantum object, not as a classical object. A classical body has a trajectory. But a quantum object has a wave, a wave-length, produces interference as a wave. In the atom, the movement of the electron doesn't fit the classical laws of movement, i.e. rotates with some velocity around the nucleus. It is even difficult for us to say if it rotates. The best description we can give for the dynamics of the electron in the atom, is the wave-function.

Why is it difficult to say that it rotates? In the classical mechanics, an object that rotates around a rotation axis has an angular momentum along that axis. And in the plane perpendicular to that axis, the projection of the angular momentum is zero. But, for instance, in a hydrogen atom the electron on the lowest energy level has angular momentum zero. So, does it rotate? Hard to say.

• I'd like to add a bit of what I hope is clarification here. When one says that , "an electron behaves like a wave," it generally refers to a certain experiment or set of experiments. The property "behaves like a wave" need not carry over to other experiments. The (non scientific) usage of "an electron is a wave" would imply (I think) that all experiments should show wave-like behavior. Terms like "wave" and "particle" are human constructs; there is no physical requirement that an electron (or anything else) conform to that construct. – ttw Mar 18 '17 at 21:08
• I am sorry that I cannot add a full answer. I'll do my best within a comment. Waves or billiard-like objects are classical concepts. In the microscopic domain we have totally other creatures. The best description of these creatures is given by the wave-function. To put it in short, when the LINEAR DIMENSIONS of an object are much smaller than the wavelength of its movement, we can get interference patterns for that object - i.e. wave-like behavior. There are famous experiments of the Zeilinger team with fluoro-fullerenes and porphyrin molecules (see continuation) – Sofia Mar 20 '17 at 13:01
• These molecules are big, and for obtaining interference with them, their velocity had to be very much reduced. In this way, the wavelength became sufficiently smaller than the linear dimensions of the molecule. But if the object is so big that there is no way to reduce its velocity sufficiently, the wavelength is much smaller than the fringe width, and there are additional problems too. – Sofia Mar 20 '17 at 13:07

When you get into quantum physics things start to get a little strange - to say the least. What you have to understand is that electrons (or any other particles for that matter) are simply modelled as particles because that matched most closely with their behaviour, as understood at the time.

As we have developed a better understanding of quantum mechanics, we understand that the particle model simply does not describe the observed phenomena well enough. We do, however, realise that some of the qualities of electrons can be described by wave theory.

I personally don't think it's correct to say an electron is a wave, simply that it behaves like a wave. In quantum mechanics, in order to begin to understand it, you need to suspend a great chunk of what you have considered to be axiomatic thus far (i.e. that particles are particles and waves are waves).

• And what is the difference between being a wave, and behaving as a wave? There is a saying in my country: what looks as a cat, walks as a cat, and miaws as a cat, it's most probably a cat. – Sofia Dec 22 '14 at 12:20
• But what is a cat? There is no fundamental law in the Universe that describes a cat. It is simply a theoretical construct that we use to describe an entity with certain characteristics, so that we can make sense of the world (i.e. to determine if the entity is a threat). By the same token, what is a wave? A wave is simply a mathematical construct that we use to describe certain behaviours that we observe. It doesn't matter whether an entity is a wave or not, the point of physics is to describe what we observe in order to make predictions about future events. – Nick Dec 30 '14 at 11:01
• the cat is an example which is not fit for any question. It is used by physicists to show that a macroscopic bodies cannot be in a superposition of states, e.g. $(|alive> + |dead>)/\sqrt (2)$. I agree with you in full that we have to distinguish between the phenomenon that occurs in the nature, and what we are able to describe on the paper, especially for such delicate objects that seem to be disturbed when observed. But, from all our experience until now, the wave-model fits better in interference experiments than the particle model. – Sofia Dec 30 '14 at 11:16
• there are, of course, situations in which we can work with the particle model: when the wave-packet is very narrow and we don't do interference experiments. – Sofia Dec 30 '14 at 11:18
• If the cat is good enough for Schrödinger it's good enough for me ;) – Nick Dec 30 '14 at 11:20