The Method of Particular Solutions and Billiards in Linear Potentials

Matt Mahoney

Dartmouth Mathematics Dept

This talk will be a crash course on the Method of Particular Solutions as a technique for computing eigenvalues and eigenmodes of differential operators in a bounded domain Ω. The MPS has been highly successful with the Laplace operator, which can be viewed as the quantum Hamiltonian of a free particle in Ω (a quantum billiard). Preliminary results about the extension of this method to a particle in a linear potential confined to Ω will be discussed.

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