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Internal Turing Machines
Ken Loo
Using nonstandard analysis, we will extend the classical Turing machines into the internal Turing machines. The internal Turing machines have the capability to work with infinite (…
Quantum Algorithm Uncertainty Principles
Ken Loo
Previously, Bennet and Feynman asked if Heisenberg's uncertainty principle puts a limitation on a quantum computer (Quantum Mechanical Computers, Richard P. Feynman, Foundations of…
Nonstandard Feynman path integral for the harmonic oscillator
Ken Loo
we will provide a rigorous computation for the harmonic oscillator Feynman path integral. The computation will be done without having prior knowledge of the classical path. We will…
A Rigorous Real Time Feynman Path Integral
Ken Loo
Using improper Riemann integrals, we will formulate a rigorous version of the real-time, time-sliced Feynman path integral for the transition probability amplitude. We will d…