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Attend a theoretical physics seminar exploring the mathematical foundations and practical applications of Siegert states in quantum scattering theory. Learn about eigenfunctions of collision system Hamiltonians that satisfy regularity and outgoing-wave boundary conditions, encompassing bound states, complex-energy resonances, and infinitely many complex-energy states that form a discrete basis for scattering theory. Discover how Siegert pseudo-states (SPS) revolutionized the field by enabling generalization to realistic collision systems and practical computational implementation. Examine the historical development of Siegert state theory and delve into Professor Tolstikhin's groundbreaking work on SPS formulation for both stationary and nonstationary scattering scenarios. Explore how this mathematical framework eliminates continuum spectrum complications and serves as a universal tool for calculating resonances, S-matrices, and Green functions in quantum collision theory. Gain insights into the orthogonality and completeness properties of these discrete bases and their significance in modern theoretical physics applications.
