Formation of a Potential Well: Mass & Wave Interaction

[Sumarna]

How a potential well is formed? Can mass of a wave creates a potential well?

 

[collinsmark]

A potential well is anything that drops the potential energy of a particle as a function of the particle's spatial position. Potential wells might also be time varying, i.e., a potential well might be a function of both position and time.

An example of something that can cause a potential well is the Coulomb force, i.e., the force applied to an electron by a relatively stationary atomic nucleus. It's not a square potential well -- a square potential well is an idealized well that convenient for educational purposes -- but the Coulomb force does create a type of well. The electron's potential energy is less when its position is close to the nucleus. There is a potential "well" near the nucleus.

An example of a time-varying potential well could include a low-frequency electromagnetic wave applied to an otherwise stationary system. (I say low-frequency here because if the EM wave's frequency is high enough one might require quantum field theory [e.g., quantum electrodynamics] to model the resulting system.)

 

[Sumarna]

A potential well is anything that drops the potential energy of a particle as a function of the particle's spatial position. Potential wells might also be time varying, i.e., a potential well might be a function of both position and time.

An example of something that can cause a potential well is the Coulomb force, i.e., the force applied to an electron by a relatively stationary atomic nucleus. It's not a square potential well -- a square potential well is an idealized well that convenient for educational purposes -- but the Coulomb force does create a type of well. The electron's potential energy is less when its position is close to the nucleus. There is a potential "well" near the nucleus.

An example of a time-varying potential well could include a low-frequency electromagnetic wave applied to an otherwise stationary system. (I say low-frequency here because if the EM wave's frequency is high enough one might require quantum field theory [e.g., quantum electrodynamics] to model the resulting system.)

So mass of the field is not the source of a potential well?

 

[collinsmark]

So mass of the field is not the source of a potential well?

It is for a gravitational well! That is also a potential well that is used when discussing gravity.

If the discussion involves orbiting celestial bodies, for example, then yes, the potential wells are a result of bodies' masses*.

*(technically the bodies' energies, if you take it as far as general relatively [GR] --mass is just another form of energy in GR. [Edit: although gravitational potential energy doesn't necessarily count the same way as other energies in GR. But now we're moving away from the classical "well" idea, so I'll stop here. The well idea works fine though if you treat gravitational potential energy in the Newtonian context, forming a gravitational potential well.])

In my previous post I was talking about quantum theory, which ignores gravity. Quantum mechanics (QM) does deal with potential wells caused by any of the other three fundamental forces however.

 

[Sumarna]

It is for a gravitational well! That is also a potential well that is used when discussing gravity.

If the discussion involves orbiting celestial bodies, for example, then yes, the potential wells are a result of bodies' masses*.

*(technically the bodies' energies, if you take it as far as general relatively [GR] --mass is just another form of energy in GR. [Edit: although gravitational potential energy doesn't necessarily count the same way as other energies in GR. But now we're moving away from the classical "well" idea, so I'll stop here. The well idea works fine though if you treat gravitational potential energy in the Newtonian context, forming a gravitational potential well.])

In my previous post I was talking about quantum theory, which ignores gravity. Quantum mechanics (QM) does deal with potential wells caused by any of the other three fundamental forces however.

thank u a lot. i think i have understood it now :)