Definition Of "The Electron" In Quantum Mechanics

Glenn Holland

Joined Dec 26, 2014
705
Quantum mechanics (specifically the Schrodinger Wave Function) often makes reference to the most probable position of "The Electron" in an atomic orbital.

However, if the electron is actually a particle wave that extends all the way around the nucleus, it seems like the electron would be anywhere along the complete wave length. So does the term "the electron" refer to the place where the charge density is at the maximum value of the wave function?

BR-549

Joined Sep 22, 2013
4,938
I think that unless the electron, or the proton for that matter......is absorbing or excreting energy, the particle does Not have a wave function.

It has a current function. They are current loops. The electron does not orbit anything. One may always know the POSITION and MOMENTUM of an electron. Just measure the frequency.

The frequency(RPM) will tell you every property of an electron. Including the position and momentum.

Being that all loop velocity is constant......the circumference and therefore the loop RPM changes, with energy. All particles have the same tangential velocity, but different RPMs.

An atomic or dipole oscillation, is the product of two, rotating current loops.

nsaspook

Joined Aug 27, 2009
9,062

bogosort

Joined Sep 24, 2011
678
Quantum mechanics (specifically the Schrodinger Wave Function) often makes reference to the most probable position of "The Electron" in an atomic orbital.

However, if the electron is actually a particle wave that extends all the way around the nucleus, it seems like the electron would be anywhere along the complete wave length. So does the term "the electron" refer to the place where the charge density is at the maximum value of the wave function?
To quote Bill Clinton, it depends on what your definition of is is. Under the original Copenhagen interpretation, we can't say anything physically meaningful about an electron until we've measured it. To answer the question "Where is the electron?" we would have to take a measurement of its position, at which point we could say "It's right there." In terms of the Schrodinger equation, the idea goes like this: prior to measurement the only thing we know about the electron's position is that it must lie in some distribution of points, encoded by a (spatial) wave function whose amplitude corresponds to the probability of finding the electron at that point. The instant the measurement is performed, the wave function collapses to a single point, i.e., the actual position of the electron.

Though this interpretation has a no-nonsense appeal to it, and is still the default/implied interpretation most commonly used in undergraduate QM textbooks, it has largely been abandoned by practicing physicists. For one thing, no one likes a physical theory that requires unphysical elements, and in the Copenhagen line of thought the wave function is unphysical, implying that -- until it is measured -- the electron itself is unphysical! For another thing, there's no physical theory that explains the very act of wave function collapse. In essence, the Copenhagen interpretation says that things in the universe exist as (unphysical) wave functions until some observer (human?) comes along and takes a measurement, at which point the wave function is magically and irreversibly transformed into an impulse. This is a striking and unexplained asymmetry in what is otherwise a symmetrical and time-reversible theory. Even at the mathematical level this looks suspicious, as the fundamental equation of motion in QM -- the Schrodinger equation -- is both linear and unitary, yet wave function collapse is nonlinear and non-unitary.

Starting in the 1950s, physicists began describing the dynamics of QM in terms that were 100% physical. As with any scientific theory, a few fundamental assumptions had to be made, and following the logical consequences of these assumptions resulted in the various interpretations we see today, which can be grouped into three basic categories: those who believe in wave function collapse (e.g., Copenhagen); those who believe that in addition to the Schrodinger equation, there are "hidden variables" that characterize the physics of quantum objects (e.g., Bohmian mechanics); and those for whom the Schrodinger equation represents the complete picture (e.g., MWI). Note that all of these interpretations must necessarily agree on the result of any quantum measurement and the calculations involved -- after all, there is only one way to do QM; where they disagree is what's happening behind the scenes, as it were.

So, the answer to the question of what (or where) the electron is depends entirely on how you interpret QM at the behind-the-scenes level. If you're a Copenhagen dude, the electron isn't anywhere until you measure it. If you're a Bohmian fella, the electron is an ordinary particle paired with a pilot wave in a high-dimensional configuration space. And if you subscribe to MWI, then the electron is the Schrodinger equation (more precisely, it is a subset of states in the universe's Schrodinger equation).

• xox