Comment on Bessel Beams, Basis sets, Schrodinger equations, Particle-Antiparticle pairs as dark energy and matter
I was looking at Bessel beams and came across your work. You have some good methods and insights. I would like to read where you started.
Three things I was thinking about.
The Schrodinger equation is usually written in terms of spherical harmonics. But the Bessel functions could be used instead. Just as a basis.
The laser vacuum experiments are trying to focus lasers on a spot in the vacuum with sufficient energy density to spawn off electron positron pairs. I have not yet looked to see if they or anyone has tried a Bessel representation.
I have been going over lots of interferometer designs and no one so far has used Bessel beams. The problem of Gaussian beams “wobbling” at the beam focus is much of the reason for the diffraction patterns. But you could just solve for stable patterns in the focus, use that as a boundary condition and then see what it takes to sent the proper pulses into the focus to improve positron-electron pairs.
Did you know that it is possible to have stable particle-antiparticle pairs? It is my favorite for dark matter. No Coulomb field shows, no magnetic dipole field show, but it has mass. So a stable particle with no electric or magnetic field. To make it you need rotational or vibrational energy. I normally use rotational energy. The vast majority of the energy is from the 1/r^4 magnetic dipole force. That accounts for all the “nuclear” and “weak” decays. A simple magnetic dipole bond can replace most of the nuclear force with simple electromagnetic magnetic dipole approximation. it is a solution of the Shrodinger equation in first approximation. So all the particles and pairs can be made from the vacuum as stable wave solutions.
Life is really interesting.
Richard Collins, Director, The Internet Foundation