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Explore quantum tunneling phenomena in magnetic systems through this 53-minute mathematical lecture that examines the behavior of particles transitioning between deep potential wells under strong constant magnetic fields. Learn about the construction of double well potential families where low-energy eigenvalue splitting can vanish, effectively eliminating quantum tunneling in specific configurations. Discover how deforming within these potential families enables magnetic ground states to transition from symmetric to anti-symmetric configurations. Understand the conditions under which tunneling remains active in typical double wells and examine lower bounds for eigenvalue splitting in such systems. Gain insights into how these quantum mechanical principles suggest approaches for achieving enhanced band flatness in two-dimensional crystalline materials, with implications for condensed matter physics and materials science applications.
