Solving the Schrodinger Equation for the Feynman Quantum Computer

Madita Willsch

Ed Fredkin

This chapter aims to solve the problem of creating discrete, reversible systems of various equations of physics. The Schrodinger Equation involves both a first derivative with respect to time and a second derivative with respect to space. The chapter presents Ed Barton with the best starting point in what was to be his quest for the summer. He was to do a series of projects with the keystone being to find a beautiful, discrete and reversible version of the Schrodinger Equation. Ed Barton's immediate observation of the reversibility of that equation remains one of author's most striking memories of 18 years on the Massachusetts Institute of Technology faculty. Richard P. Feynman showed that by calculating the amplitude for the 0-Dimensional case in a perfectly time symmetric fashion, keeping to author's esthetic principle, then the values computed by the reversible difference equation exactly conserved the value of the amplitude.

Mohamed Said Abouelela

Xue Wang

The Feynman model is a famous theoretical model establishing the Josephson equations. Feynman et al. based on the Schrodinger equations describing the two states system of superconductor junction, have derived the differential equations of the amplitudes and phases of the two wave functions versus time, and solved them with a slightly rough method, and established the Josephson equation. It is worth considering carefully that mathematical treatment in Feynman model was not exact. In this paper we have solved the differential equations in Feynman model exactly, the results we have gotten show that A. C. Josephson equations can be established only under certain conditions..

Vicente Moret‐Bonillo

Tobias Kuna, Ludwig Streit, Werner Westerkamp

We construct the Feynman integrands for a class of exponentially growing time-dependent potentials as white noise functionals. We show that they solve the Schrödinger equation. The Morse potential is considered as a special case.