# Is free electron's motion quantized?

• sneez
In summary: This phenomenon is described by the Gell-Mann and Lowe theorem. In summary, the motion of free electrons is quantized due to the boundary conditions of the wave function. The magnetic field can cause quantization of the electron's rotation, leading to the angular momentum being quantized. There is a theory, known as the Gell-Mann and Lowe theorem, which explains how an electron can slow down or decrease in energy level without emitting a photon if the magnetic field strength is changed adiabatically. This phenomenon is described in the QED theory.
sneez
is free electron's motion quantized?

For example if i knock off electron from an atom and than trap it inside some space where i can manipulate magnetic fields, can i slow and speed up the electron continuously, or will the electron speed be quantized?

please, explain why is it quantized?

Any quantization arises from the boundary conditions of the wave function. Of course, in the case of the magnetic field (in a semi-classical picture), you'll find some sort of quantization of the rotation around the magnetic fields because the particles rotate around them and the angular momentum is quantized.

Quantization is a consequence of various kinds of boundary conditions, usually.

That makes sense, thank u

I would like to extend the question.

Can electron moving in quantized circular obit 'slow down' or decrees in energy level other way than by emitting a photon?

For example is there i way to slow down an electron by the magnetic fields 'continuously' until it will make 'jump' to lower orbit without emitting a photon?

in general: is the only way to change orbitals to emit photons? or is there another way without emitting the photon?

I would like to extend the question.

Can electron moving in quantized circular obit 'slow down' or decrees in energy level other way than by emitting a photon?

For example is there i way to slow down an electron by the magnetic fields 'continuously' until it will make 'jump' to lower orbit without emitting a photon?

in general: is the only way to change orbitals to emit photons? or is there another way without emitting the photon?

The most accurate forum for the discussion of interaction of particles and fields is QED, however QED is very ambigous when it comes to bound state problems. You can adiabatically change the strength of a magnetic field within a first quantised theory and the energy eigenvalues will change continuosly. If it done adiabatically as zero temperature then the particle will remain in the ground state, its energy changing continuously. There is a thery by Gell-mann and Lowe with regard to this.

In QED, External field need not be quantised and as such I would say that yes, this would be possible. The particle will remain in the ground state without the emission of a photon if the potential is altered adiabatically (very slowly such that the system reamins in equilibrium).

## 1. What does it mean for an electron's motion to be quantized?

Quantization of an electron's motion refers to the phenomenon of the electron being confined to specific energy levels or orbits within an atom. This means that the electron can only exist at certain discrete energy levels and cannot exist in between these levels.

## 2. Why is free electron's motion quantized?

The quantization of a free electron's motion is a result of the fundamental principles of quantum mechanics. According to these principles, particles such as electrons can only exist at discrete energy levels and cannot exist in between these levels.

## 3. How does the quantization of an electron's motion affect its behavior?

The quantization of an electron's motion significantly affects its behavior. This phenomenon is responsible for many fundamental properties of matter, such as the stability and structure of atoms, the formation of chemical bonds, and the behavior of solids, among others.

## 4. Can the quantization of an electron's motion be observed in everyday life?

Yes, the quantization of an electron's motion can be observed in everyday life through various phenomena such as the discrete emission spectrum of elements, the energy levels of electrons in semiconductors and metals, and the behavior of electrons in magnetic fields.

## 5. What are the practical applications of understanding the quantization of an electron's motion?

Understanding the quantization of an electron's motion has led to numerous technological advancements in fields such as electronics, materials science, and chemistry. Some practical applications include the development of transistors, lasers, and computer memory devices.

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