Mathematical Sciences: Spectral Properties of a Random Schrodinger Operator

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This research planning grant supports the research of Professor Christ to study the Stark-Hamiltonian with random potentials over the real numbers. In particular she will study the spectrum of the Stark-Hamiltonian and their resonances. Modern physics, quantum mechanics and relativity, is a product of the twentieth century. It is founded firmly in the last century's attempt to address the microstructure of matter and to come to grips with the concepts of action-at-a distance, electro- magnetism, and heat radiation. The mathematical foundations for these developments, collectively called mathematical physics, ranges from detailed analysis of Schrodinger operators, which governs the dynamics of particles, to unified field theory, which attempts to unite the four known forces into a single theory.