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

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In summary, the book mentioned implicitly it doesn't, but why?In summary, the book mentioned implicitly that if a photon just passes thru the slab and doesn't change wavelength, it does not belong to Rayleigh's scattering.
  • #1
kof9595995
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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,
[tex]E = \pm \sqrt {m_0^2{c^4} + {p^2}{c^2}} [/tex]
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.
 
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  • #2
kof9595995 said:
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,
[tex]E = \pm \sqrt {m_0^2{c^4} + {p^2}{c^2}} [/tex]
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.
 
  • #3
Well, thanks for reply first.
olgranpappy said:
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?


olgranpappy said:
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.
 
  • #4
kof9595995 said:
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.
 
  • #5
Hi kof9595995! Hi olgranpappy! :smile:
kof9595995 said:
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.
olgranpappy said:
little by little one travels far.

goldfish don't! :smile:

I'm quite happy with simple harmonic motion! :biggrin:
 
  • #6
Ok,thanks guys, you really release me from the very uncomfortable feeling about Dirac's sea concept.
 
  • #7
Another soul rescued from the sea! o:) :biggrin:
 

1. What is Compton's scattering and how does it relate to quantum physics?

Compton's scattering is a phenomenon in which a photon (a particle of light) collides with an electron, resulting in a change in the photon's wavelength and energy. This phenomenon is important in quantum physics because it provides evidence for the particle-like nature of light and the concept of wave-particle duality.

2. Can you explain the equation for Compton's scattering?

The equation for Compton's scattering is given by Δλ = h/mc(1-cosθ), where Δλ is the change in wavelength of the scattered photon, h is Planck's constant, m is the mass of the electron, c is the speed of light, and θ is the angle between the initial and final direction of the photon. This equation shows that the change in wavelength is directly proportional to the electron's mass and the photon's energy, and inversely proportional to the speed of light.

3. How does Dirac's relativistic energy equation differ from Einstein's famous equation, E=mc²?

Dirac's relativistic energy equation, E = √(p²c² + m²c⁴), takes into account the momentum (p) of a particle, while Einstein's equation, E=mc², only considers the particle's rest mass (m). This means that Dirac's equation is more accurate for high-speed particles, such as those in quantum physics, while Einstein's equation is more accurate for low-speed particles.

4. Can you explain the concept of spin in quantum physics?

In quantum physics, spin is a fundamental property of particles that describes their intrinsic angular momentum. It is often visualized as the particle spinning on its own axis, but in reality, it is a purely quantum mechanical property with no classical analog. Spin plays a crucial role in the behavior and interactions of particles, and it is an important concept in understanding quantum systems.

5. What is the significance of the Dirac equation in quantum physics?

The Dirac equation is a relativistic wave equation that describes how particles with spin behave in a quantum system. It is significant in quantum physics because it successfully incorporates both special relativity and quantum mechanics, providing a more accurate description of particles at high speeds. It also predicted the existence of antimatter, which was later confirmed by experiments. The Dirac equation is still used today in various areas of theoretical and experimental physics.

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