175(7): New Fundamental Equation of Quantum Mechanics

This is Eq. (8), introducing the anticommutator of x and p at a fundamental level. Numerical results so far show that this anticommutator is zero for all the wavefunctions of the harmonic oscillator and the particle in a box, two of the well known exact solutions of the Schroedinger equation. In angular motion it is well known that the anticommutators of the Pauli matrices are zero, so are anticommutators of rotation generators and angular momenta. There is a link between rotation generators and the anticommutator {x, p} psi. So for the harmonic oscillator and particle in a box, the commutator of x and p is non zero while the anticommutator of x and p is zero for the same wavefunctions. This means that x squared and pp = p squared can be “specified simultaneously” in the Copenhagen claim, while x and p cannot. So in the Copenhagen claim p may be unknowable if x is specified precisely and pp completely knowable when x squared is specified precisely. This an absurd result, so Copenhagen is refuted. In ECE these results emerge from the Schroedinger equation as interpreted originally by Schroedinger, i.e. delta x and delta p are statistical in nature, no more than that.

a175thpapernotes7.pdf