Quantum mechanics problems in observer's mathematics
Abstract
This work considers the ontology, guiding equation, Schrodinger's equation, relation to the Born Rule, the conditional wave function of a subsystem in a setting of arithmetic, algebra and topology provided by Observer's Mathematics (see <monospace>www.mathrelativity.com</monospace>). Observer's Mathematics creates new arithmetic, algebra, geometry, topology, analysis and logic which do not contain the concept of continuum, but locally coincide with the standard fields. Certain results and communications pertaining to solutions of these problems are provided. In particular, we prove the following theorems: Theorem I (Twoslit interference). Let Ψ_{1} be a wave from slit 1, Ψ_{2}  from slit 2, and Ψ = Ψ_{1}+Ψ_{2}. Then the probability of Ψ being a wave equals to 0.5. Theorem II (kbodies solution). For W_{n} from mobserver point of view with m>log_{10}((2×10^{2n}1)^{2k}+1), the probability of standard expression of Hamiltonian variation is less than 1 and depends on n,m,k.
 Publication:

9th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences: ICNPAA 2012
 Pub Date:
 November 2012
 DOI:
 10.1063/1.4765537
 Bibcode:
 2012AIPC.1493..518K
 Keywords:

 algebra;
 geometry;
 probability;
 Schrodinger equation;
 topology;
 wave functions;
 02.40.Re;
 02.50.Cw;
 03.65.Fd;
 03.65.Ge;
 03.65.Ta;
 Algebraic topology;
 Probability theory;
 Algebraic methods;
 Solutions of wave equations: bound states;
 Foundations of quantum mechanics;
 measurement theory