Quantum Mechanical Scattering (3D) - What about forward scattering?

In summary, the standard way to solve the 3D scattering problem in nonrelativistic QM is to consider an incident plane wave encountering a scattering potential, resulting in an outgoing spherical wave. The differential cross section only accounts for the scattered wave, but there is also interference with the un-scattered incident wave in the forward direction. This relation is discussed in QM textbooks on scattering, such as Roger Newton's Scattering Theory of Waves and Particles.
  • #1
maverick280857
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Quantum Mechanical Scattering (3D) -- What about forward scattering?

Hi

In nonrelativistic QM, the standard way to solve the 3D scattering problem is to consider an incident plane wave [itex]\psi(z) = Ae^{ikz}[/itex] which encounters a scattering potential, producing an outgoing spherical wave having the asymptotic form

[tex]\psi(r, \theta, \phi) = A\left\{e^{ikz} + f(\theta,\phi)\frac{e^{ikr}}{r}\right\}[/tex]

This of course corresponds to

[tex]\frac{d\sigma(\theta,\phi)}{d\Omega} = |f(\theta, \phi)|^2[/tex]

My question is: in the "forward" direction ([itex]\theta = 0[/itex]) we have both the scattered wave as well as some of the incident wave that hasn't been scattered. But the differential cross section above only corresponds to the scattered wave. How does one mathematically account for the ticks a detector placed in the forward direction will register due to the un-scattered incident wave?

Thanks.
 
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  • #2


Have you taken a look at Roger Newton's Scattering Theory of Waves and Particles ?
 
  • #3


The scattered and incident waves interfere in the forward direction.
This leads to a relation between I am f(0) and the total cross section.
It should be discussed in any QM textbook that considers scattering.
 

Related to Quantum Mechanical Scattering (3D) - What about forward scattering?

1. What is quantum mechanical scattering?

Quantum mechanical scattering is a phenomenon that occurs when particles interact with each other or with a potential energy barrier. It involves the exchange of energy and momentum between the particles, and is described by the laws of quantum mechanics.

2. How is quantum mechanical scattering different from classical scattering?

Quantum mechanical scattering takes into account the wave-like nature of particles, whereas classical scattering only considers the particle-like behavior. Additionally, in quantum mechanical scattering, the particles can exist in superposition states, meaning they can be in multiple places at once, while in classical scattering, the particles have a well-defined position.

3. What is forward scattering?

Forward scattering is a type of scattering where the scattered particles move in the same direction as the incident particles. This means that the angle of scattering is equal to or close to zero degrees.

4. How is forward scattering important in quantum mechanics?

Forward scattering is important in quantum mechanics because it can provide information about the potential energy of the particles involved in the scattering process. The amount of forward scattering can also indicate the strength of the interaction between the particles.

5. What are some potential applications of forward scattering in quantum mechanics?

Forward scattering has various applications in quantum mechanics, such as in the study of atomic and molecular collisions, particle interactions in high-energy physics, and the characterization of materials through techniques like Rutherford backscattering spectroscopy. It is also used in quantum computing and cryptography.

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