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dev70
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HI PF, I wanted to know what are the degrees of freedom of an electron? How should it behave when it is left with its least energy in vacuum?
In classical theory, the lowest possible energy would be if electron stood still anywhere inside the box, with zero velocity.if we take up a thought experiment like a particle in a box (let the particle here be an electron) and if the electron has the lowest possible energy i.e., zero point energy then how would the electron behave then?
Jano L. said:In quantum theory, the answer depends on the interpretation one chooses. In addition to the point of view of Jazzdude, there is also a point of view according to which the particle jiggles back and forth in a chaotic motion, even at zero temperature
Jano L. said:It is not more complicated than how statistical physics works. We use probability density function of possible configurations to evaluate likelihood (probability) that the system has some definite configuration. In the model, the system (say, gas) is supposed to always have some, we just do not know which, so we assign probabilities.
In quantum theory, this approach is called statistical interpretation. The core of this approach is the Born rule for Schroedinger's wave function:
the value of [itex]|\psi(\mathbf r)|^2\Delta V[/itex] gives the probability that the particle is at position [itex]\mathbf r[/itex].
Similar rule can be stated for wave function describing many-electron atom.
The particle can be thought to exist and have definite position and momentum - we just do not know which. See great article by L. Ballentine, Statistical Interpretation of Quantum Mechanics, esp. the end of the page 361.
http://rmp.aps.org/abstract/RMP/v42/i4/p358_1
Similar point of view is adopted by Bohm's theory.
do these electrons have enough energy to convert virtual particle to real one and thus radiate?
And I think you put a little too much into the statistical interpretation.
What you describe is definitely not Bohm
The idea of random walks has been given up long ago, simply for the reason that it doesn't work out.
Jano L. said:In quantum theory of light, the expression "system radiates" means basically "system loses energy". If the whole system electron + box was in its lowest ground state, there is no way the system could lose more energy, so in theory the box would not radiate to the outside. However, you want to know what happens to the electron inside. Now the electron is not isolated and not in ground state (only the whole large system is). It can lose energy to the wall if it has some; or accept some from the wall. One can imagine this as a chaotic exchange of energy between the electron and the wall.
However, I want to point out that such isolating wall does not exist and there is always interaction with the surroundings. So even the box itself will radiate to the outside and be able to exchange energy.
dev70 said:Does that mean electrons motion won't cause the vacuum fluctuations to be able to convert virtual particle to real ones?
andrien said:This is more or less rubbish.there are no virtual particles,it is possible to formulate quantum electrodynamics without virtual photon type thing.
Depends on what you mean by energy. In quantum theory, there are states which are not eigenstates of the Hamiltonian and there are people who refuse to assume it has a meaning for such states. Then the question is dissolved, energy does not exist, hence no question about its conservation.Some say it means energy conservation can be violated for some time some say its not possible. I am stuck at that point. Whats the reality?
The degrees of freedom for an electron refers to the number of independent variables that can affect its motion or state. This concept is important in understanding the behavior of electrons in different systems and environments. Here are five frequently asked questions about the degrees of freedom for an electron:
An electron has three degrees of freedom, which are related to its movement in three-dimensional space. These degrees of freedom are usually described as the electron's position in the x, y, and z directions.
The spin of an electron is considered an additional degree of freedom, bringing the total to four. The spin of an electron can have two possible states: spin up or spin down. This additional degree of freedom plays a crucial role in many quantum mechanical phenomena.
Yes, all electrons have the same number of degrees of freedom. This is a fundamental property of electrons, and it does not change regardless of their location or environment.
The degrees of freedom for an electron determine its ability to move and interact with other particles in a system. For example, an electron in a solid has limited degrees of freedom compared to an electron in a gas, which can move freely in all directions.
The degrees of freedom for an electron can be altered by external factors such as temperature, electric and magnetic fields, and interactions with other particles. These changes can affect the electron's behavior and properties, making the concept of degrees of freedom crucial in many fields of physics and chemistry.