On Saturday, September 13, 2025 at 6:24:16 AM UTC-6 John Clark wrote:
On Sat, Sep 13, 2025 at 7:19 AM Alan Grayson <[email protected]> wrote: *>> Schrodinger's Equation describes how fermions behave quantum mechanically. * *> I've solved it many times and never saw any reference to fermions.* *I find that extremely difficult to believe. Schrodinger's equation describes how non-relativistic fermions behave. Dirac's Equation describes how fermions behave if special relativity is taken into account, and Dirac can be simplified down to Schrodinger's equation in cases where Special Relativity is not important. And all the solutions to the Dirac equation, and thus Schrodinger's Equation too, must obey Fermi-Dirac statistics and the Pauli Exclusion Principle.* *>> A macroscopic object, such as a polarizer, is made out of fermions. * *> No bosons in a polarizer? AG* *For massless spin-1 bosons, such as photons, you can use Maxwell's Equations, and they enable you to derive Malus's Law which says that the transmitted intensity of a beam of light that can make it through a polarizer is I = I₀ cos²(θ) where θ is the angle between the incident polarization and the polarizer axis. And if a beam of light is made out of photons then the probability of a single photon making it through a polarizer must be cos²(θ).* *To summarize, for a beam of light with N photons:* - *Quantum prediction: On average, N × cos²(θ) photons pass through* - *Classical prediction: cos²(θ) fraction of the intensity passes through* - *These are the same thing.* * John K Clark See what's on my new list at Extropolis <https://groups.google.com/g/extropolis>* Check this out. As I expected; no reference whatsoever to fermions. AG https://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion visit https://groups.google.com/d/msgid/everything-list/bd5a4569-8674-4ad8-b8d0-762e70f233bbn%40googlegroups.com.
