Graduate Is There a Closed Form for Airy Disk Eigenfunctions?

Click For Summary
The discussion centers on the search for a closed form of the eigenfunctions of the Airy disk function, specifically the Bessel function J_1(x)/x. Participants note that, based on existing literature, a closed form likely does not exist. Most publications focus on approximations, such as the first zero and angle calculations, rather than providing a definitive closed form. The consensus suggests that while the topic is well-explored, it remains unresolved. Therefore, the quest for a closed form of Airy disk eigenfunctions continues without conclusive findings.
marcusl
Science Advisor
Messages
2,965
Reaction score
672
Does anyone know if the eigenfunctions of the Airy disk function (or Bessel function) \frac{J_1(x)}{x} has a closed form?
 
Physics news on Phys.org
From what I have seen on the internet, the answer is probably no. There are many publications and neither mentioned one, only approximations like the first zero and calculation of angles.
 

Thread 'Confusion about the Moyal-Weyl twist'

I am studying the mathematical formalism behind non-commutative geometry approach to quantum gravity. I was reading about Hopf algebras and their Drinfeld twist with a specific example of the Moyal-Weyl twist defined as F=exp(-iλ/2θ^(μν)∂_μ⊗∂_ν) where λ is a constant parametar and θ antisymmetric constant tensor. {∂_μ} is the basis of the tangent vector space over the underlying spacetime Now, from my understanding the enveloping algebra which appears in the definition of the Hopf algebra...
View full post »

Similar threads

Undergrad Validity of identical eigenfunction of commutating operators
  • · Replies 12 ·
Replies
12
Views
692
Undergrad Does a Polarizer Alter the Shape of Airy Disks in Optical Systems?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Completeness of Eigenfunctions of Hermitian Operators
  • · Replies 22 ·
Replies
22
Views
2K
Graduate Angular momentum uncertainty principle and the particle on a ring
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Lateral offset from a centered star as measured at the focal plane
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad Particle in the box eigenfunctions
  • · Replies 60 ·
3
Replies
60
Views
8K
Undergrad Deriving the time-dependent wave equation from Energy eigenfunctions
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Obtain simultaneous eigenfunctions?
  • · Replies 1 ·
Replies
1
Views
2K
Stretched spring attached to the center of a pure rolling disk
  • · Replies 11 ·
Replies
11
Views
1K
Undergrad Why Does the First Eigenfunction Have a Zero in Sturm-Liouville Problems?
  • · Replies 1 ·
Replies
1
Views
2K