# Electron waves through conductors

I'm not a student, professor, or academic scholar so please excuse me if this question seems "amateur". I'm very curious about how electricity, magnetism, and frequency all work together.

From my understanding level, an electron is not too much like an actual particle. An "electron" is really like a standing wave of energy, which based on the energy level of the orbital it has a certain frequency at which the waves radiate back and forth from the nucleus. The further out these waves go the more energy the particular element has.

When we apply voltage and current to a conductor and make these "electrons" travel through a wire doesn't that mean that the actual energy from each atom is passing from one nucleus to another and not a particle of any sort? How do the "electron waves" not become disrupted while physically moving in a certain direction?

Also if the electron is more of a standing wave than how can we label this "wave" as having a negative charge? Does that mean that all energy is of negative charge and anything with a positive charge is considered having zero energy and that's why the negative energy wants to fill it in?

Also, if hydrogen only has one energy shell than how can we consider that a wave at all when a wave is defined by a high and low point alternating together?

Any and all answers are much appreciated

From my understanding level, an electron is not too much like an actual particle. An "electron" is really like a standing wave of energy, You have a lot of misunderstandings:

An electron is an elementary particle in the quantum mechanical model of particle physics, a point particle with spin and mass assigned to this point. Its footprint looks like a particle (the dots in the top frame) and it leaves tracks like a particle in a bubble chamber for example of a detector.

The frequency associated with quantum mechanical particles is a frequency seen only in the probability distrubution, which is predicted by the solutions of quantum mechanical equations.

which based on the energy level of the orbital it has a certain frequency at which the waves radiate back and forth from the nucleus. The further out these waves go the more energy the particular element has.

Now you mix up an electron bound in an atomic unit, around a nucleus. Your description is not useful. What is useful is the concept of orbitals, probability loci for the electron about a nucleus. Here are possible orbitals of a hydrogen atom.

An electron in a higher orbital needs less energy to be supplied so it can get free.

When we apply voltage and current to a conductor and make these "electrons" travel through a wire doesn't that mean that the actual energy from each atom is passing from one nucleus to another and not a particle of any sort? How do the "electron waves" not become disrupted while physically moving in a certain direction?

No. There are no physical waves as you imagine, and certainly no atom to atom exchanges. Solids are modeled quantum mechanically with the band theory

There exists a conduction band, where the electrons are common to the whole system in the conductor crystal structure, not to individual atoms.

A useful way to visualize the difference between conductors, insulators and semiconductors is to plot the available energies for electrons in the materials. Instead of having discrete energies as in the case of free atoms, the available energy states form bands. Crucial to the conduction process is whether or not there are electrons in the conduction band. In insulators the electrons in the valence band are separated by a large gap from the conduction band, in conductors like metals the valence band overlaps the conduction band, and in semiconductors there is a small enough gap between the valence and conduction bands that thermal or other excitations can bridge the gap.

So you see that it is the whole lattice that responds to changes in voltage in a solid, and the electrons that move out of the solid in a current carrying wire are replaced from the voltage source in a continuous manner, so the solid remains neutral.

What is waving at the individual electron level is its probability distribution. A collective classical wave in real space time , like an AC current can be induced by the superposition of a large number of electrons, but it can be simply described by classical electricity and magnetism equations, no need to go to individual electrons, though there is mathematical continuity.

Also, if hydrogen only has one energy shell than how can we consider that a wave at all when a wave is defined by a high and low point alternating together?

The alternations in space happen in the complex number function called the wave function $$Ψ$$, a solution of the Schrodinger equation , it is $$Ψ*Ψ$$ that is waving , the probability distribution , not the electron itself, as seen in the double slit experiment above, the interference pattern appears in the accumulation. That is why particle experiments accumulate data with the same initial conditions in order to test the validity of theories.

• Thank you very much for taking the time to help me clear some of that up. I will continue learning based on the information you provided. – K. Murph Jan 10 at 4:31

Electrons exhibit wave-like AND particle-like behaviour depending on the situation. Modern descriptions of conductors and currents in them are based on both of these aspects of electrons nature. So in a conductor, lets say a perfect one without any thermal disruptions, where metal ions are perfetly still, electrons are in some sort of periodic potential. When bound just to one nucleus they are actually in a sort of Coulomb potential. To be in a potential means just to be in interaction with some body. In this example, we can say that electron is under the influence of a nucleus and is bound to it. So, if now we have many nuclei, it will be a bit different. Now the electron is in some sort of periodic potential because in a metal ions are spaced regularly and forming sort of a crystal structure. In this periodic structure electrons are described like waves with certain propertis. Functions describing these waves are called Bloch functions. What is interesting is that these Bloch functios are almost like functions which describe totaly free electrons. So, in such a structure electrons are free to move arround and there is no resistance. Resistance comes when this periodicity of a crystal is disrupted. It can be disrupted by thermal motion or by imperfections, edge effects because after all, crystal is not infinite, right. Quantum mechanics in its core is not actually about waves. It is about strange behaviour of properties of radiation and matter during interactions with their surroundings. Yes, Schrodinger equation is a wave equation, but that is not all. The point is in the experiments and to undertand QM go and read about experients. Double-slit experiment, Stern-Gerlach experiment...etc. In short, what is important when talking aboutwave nature of particles, is the double slit experiment. In this experiment we observe that electrons travel from their source to the screen and on the screen they form a pattern. We can see where these electrons hit the screen so they are particle-like entities. Because you have definite locations on the screen. But, the pattern as a whole, looks like the pattern for wave interference. Meaning, there are regular stripes of more dense and less dense electron agregation on the screen. So, this is even possible when only one electron at a time travels from the source to the screen. So each electron nteracts with it self on the way meaning that somehow it passes through both slits at the same time, just like a water wave would. So what we conclude is that electrons position is not definite but it is spread in space as a function of some coordinates. So when this electron hits the detector screen it suddenly localizes itself in some place as a consequence of interaction with the screen. Point is, without interaction with environment, electrons position is not definite, it has no definite position and then, suddenly, when it hits detector, it has to decide. And what electron decides is what shows on the screen and what Schrodinger equation gives is probability of a decision. What is funny is that this probabilita is described with a wave function and if two electrons interfere then these probabilities add up at one point in space. Of course, this decision making of the electron is strange stuff. If you want, instead of decision made by the electron, we can say, electron as a system, collapses from many posibilities to just one and what will that one be is defined by some probability function in space. So electron exists as a wave not like some vibrating string but its probability of position is described with some function which is a wave function. This probability of position is effected and changed by interactions, such as the interection with a proton to form a hydrogen atom.