Questions on Quantum Physics: Compton's Scattering & Dirac's Relativistic Energy

[kof9595995]

Just start my QM1 course,and our textbook is "Quantum Physics-of atoms,molecules,solids, nuclei,and particles" by Robert Eisberg and Robert Resnick.
Here are 2 of the questions bothering me recently:
1. In Compton's scattering experiment, if the photon's wavelength doesn't change in scattering, we say it belongs to Rayleigh's scattering. My question is, if a photon just passes thru the slab and doesn't change wavelength, does it belong to Rayleigh's scattering? The book mentioned implicitly it doesn't, but why?
2.In Dirac's consideration about relativistic energy of electrons,
E = \pm \sqrt {m_0^2{c^4} + {p^2}{c^2}}
and he said the negative energy levels are fully occupied, but since momentum p is arbitrary, the energy levels should be continuous, is that right?
If so, we need infinite many electrons to occupy them, but if there are infinite many, the global version of charge conservation won't make sense any more, it would be weird to me.
Thanks in advance.

 

[olgranpappy]

Just start my QM1 course,and our textbook is "Quantum Physics-of atoms,molecules,solids, nuclei,and particles" by Robert Eisberg and Robert Resnick.
Here are 2 of the questions bothering me recently:
1. In Compton's scattering experiment, if the photon's wavelength doesn't change in scattering, we say it belongs to Rayleigh's scattering. My question is, if a photon just passes thru the slab and doesn't change wavelength, does it belong to Rayleigh's scattering? The book mentioned implicitly it doesn't, but why?

if it doesn't change direction or energy then it simply did not scatter at all... hence it did not Rayleigh scatter.

2.In Dirac's consideration about relativistic energy of electrons,
E = \pm \sqrt {m_0^2{c^4} + {p^2}{c^2}}
and he said the negative energy levels are fully occupied, but since momentum p is arbitrary, the energy levels should be continuous, is that right?
If so, we need infinite many electrons to occupy them, but if there are infinite many, the global version of charge conservation won't make sense any more

Those fully occupied negative energy levels were a convenient fiction at the time Dirac invented his equation. The interpretation of the Dirac equation as a single particle wave equation is not consistent, thus the Dirac equation will have to wait until you study QFT to fully make sense.

 

[kof9595995]

Well, thanks for reply first.

if it doesn't change direction or energy then it simply did not scatter at all... hence it did not Rayleigh scatter.

So we can't take it as an extreme case?OK, then another question related: what's the difference if I interpret Compton scattering as collision between photon and electron(the textbook version), or the electron absorb the photon and emit another photon instantly(my hypothetical version). Can there be any observable difference between two interpretations?Or my version is forbidden by some principle I don't know yet?

Those fully occupied negative energy levels were a convenient fiction at the time Dirac invented his equation. The interpretation of the Dirac equation as a single particle wave equation is not consistent, thus the Dirac equation will have to wait until you study QFT to fully make sense.

Wow, that's way to go for me.

 

[olgranpappy]

Well, thanks for reply first.

So we can't take it as an extreme case?OK, then another question related: what's the difference if I interpret Compton scattering as collision between photon and electron(the textbook version), or the electron absorb the photon and emit another photon instantly(my hypothetical version). Can there be any observable difference between two interpretations?

I don't know, but then again I don't really know anything about "your version". Is there any difference between your version and the textbook version other than the verbiage of your description?

For starters I would stick with learning the fundamentals from the textbook. This will serve you well in the future. Once you know the textbook version then you will be better equipt to answer your own question regarding your own version of events.

Wow, that's way to go for me.

little by little one travels far.

 

[tiny-tim]

Hi kof9595995! Hi olgranpappy!

2.In Dirac's consideration about relativistic energy of electrons,
…
he said the negative energy levels are fully occupied…

That's the "Dirac sea" interpretation, which was fairly soon rejected, including by Dirac himself.

See http://en.wikipedia.org/wiki/Dirac_sea#Inelegance_of_Dirac_sea …

The development of quantum field theory (QFT) in the 1930s made it possible to reformulate the Dirac equation in a way that treats the positron as a "real" particle rather than the absence of a particle, and makes the vacuum the state in which no particles exist instead of an infinite sea of particles. This picture is much more convincing, especially since it recaptures all the valid predictions of the Dirac sea, such as electron-positron annihilation. On the other hand, the field formulation does not eliminate all the difficulties raised by the Dirac sea; in particular the problem of the vacuum possessing infinite energy.

little by little one travels far.

goldfish don't!

I'm quite happy with simple harmonic motion! ​

 

[kof9595995]

Ok,thanks guys, you really release me from the very uncomfortable feeling about Dirac's sea concept.

 

[tiny-tim]

Another soul rescued from the sea!