As always, please be relaxed and have some beverage before reading this blog, Sirs.
I am wondering about the way an electron exists and about the way the electron moves in an atom or in a molecule.
It is written in a preface of a book "Quantum Divide" by C. G. Gerry and K. M. Bruno that when we think about an electron in a hydrogen atom, we often image it like a particle orbitting about the proton. Surely, It is certain that it is really a very comprehensible picture for a hydrogen atom. But this classical Bohr model was replaced by the succeeding modern quantum mechanical description which states that there is only probability for finding the electron at one place.
The quantum mechanics denies sich a simple picture of "orbitting electron." The quantum mechanics only gives us a set of rules and a set of equations for calculating some value of an attribute of a system.
The quantum mechanics gives us only the probability. So we are inclined to suppose that an electron can be here and there simultaneously around the nucleus. But is it possible for an electron to exist on two places or on many places at once? "No," says the book, "It is not quite accurate to say that even a quantum particle can be in two places at once. The things are much more subtle than that."
Much more subtle than that? Then we cannot but inquire "what is it at all?" If it were to be the case, then how should we image the way the electron exists? How should we image the way the electron moves? The quantum mechanics keeps the secret and only gives us the probability P1 of finding an electron at a position x1.
It reminds us of the paradox of Zeno. Another book by John Gribbin taught me about that paradox. The Greek philosopher Zeno of Elea asked: "An archer has fired an arrow to shoot a deer. The deer has run away. Thinking every instants, the fired arrow can never be at two places at once. So the arrow is definitely at one place at a time. Therefore the arrow cannot reach the deer?"
The same thing can be said about the motion of an electron described by quantum mechanics. It says only that for an electron there is only the probability P1 at place x1, the probability P2 at place x2,..., and so on.
Then we ask naturally:"How does an electron move from the position x1 to the position x2, from the position x2 to the position x3,... and so on?" Everyone wishes to see the mental picture of the quantum world which the quantum mechanics might be able to paint.
Or does the quantum mechanics completely defy our any attempt to see such a picture? Can't the words or the logics of our everyday experience be used for explaining the behavior of any quantum mechanical entity?
How do you think, Sirs?
Thank you for reading
You have asked an interesting question that is difficult to answer. You are correct in assuming that the Bohr model can be thought of in terms of an electron, as a particle, circling a proton, as a particle. But remember that this is a "model," it is not "correct" or "true." It is nothing more than one way of thinking about the structure of an isolated hydrogen atom. And it has been replaced by quantum mechanical "models" of individual atoms and the distribution of electrons in molecules. Once again, not something that is either "correct" or "true." But another way of thinking about an atom.
When Schrodinger developed his model of the atom, he started with a mathematical equation that describes the behavior of a "wave" from classical physics. He then tried to substitute some of the properties of a particle into this wave equation. (The previous sentence is an attempt to express in relatively simple language what is, in fact, a more complex idea, but let's try to avoid the details.) The net result was a mathematical equation that can be "solved." But the term "solved" is interesting because the typical problems students encounter in mathematics can be solved for a single answer. Or, in cases such as the quadratic formula, two answers. Schrodinger's equation can be solved for many answers described by different sets of three quantum numbers specified by the "rules" you mentioned.
For reasons we don't have room to describe, evaluating the square of one of these mathematical functions at a particular place in space or, perhaps more accurately, for a given volume in space gives you the probability that the electron would be located at that place or in that volume at a given moment in time, IF the electron behaved the way the mathematical equation behaved.
Is the result of solving the Schrodinger equation "correct" or "true?" No. It is a model; another way of thinking about the atom.
Is the electron a "particle" that occupies space? No. Is it a "wave" that travels through space? No. One of the steps toward the quantum mechanical model of the atom assumed it is a "wave-particle." Is that true? No. It is something that exists that we find useful to think about as if it was a mixture of a wave and a particle. But that, once again, is only a "model" because there is nothing that exists on the scale of objects visible to the eye that has these properties.
Here is an interesting way to think about the electron on an a hydrogen atom. We'll put a single hydrogen atom inside a magnetic field. Classical physics assumes that electricity and magnetism are coupled. So we now have an atom with a single electron inside a magnetic field. Using the connection between electricity and magnetism from classical physics, we can assume that the magnetic field causes the electron to move around the proton. Not the way a particle would move. But we can think about the electron as being spread out in space and this spread out electron density now starts to move around the proton. This is interesting because we can find experimental evidence consistent with the idea that this happens.
So, instead of asking whether the electron can be in two places at the same time, let me try a metaphor that I haven't seen anyone else use. Take a knife and spread some peanut butter on a piece of bread. Is the peanut butter a "particle?" No. Is it a "wave?" No. Is it a "wave-particle?" No. What it is, is a spread out "something" that moves through space as we put it into our mouth.
I hope this helps.