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One-dimensional reflection in the quantum mechanical bootstrap
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We describe the application of the quantum mechanical bootstrap to the solution of one-dimensional scattering problems. By fixing a boundary and modulating the Robin parameter of the boundary conditions we are able to extract the reflection coefficient for various potentials and compare to physical expectations. This includes an application of semidefinite programming to solving a half-line Schrodinger problem with arbitrary Robin boundary conditions. Finally, the WKB approximation is used to numerically determine the scattering behavior of the exponential potential of Liouville theory.
Forward citations
Cited by 2 Pith papers
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Stationarity is not enough: tightness of the quantum mechanical bootstrap and the copositive cone
The stationary quantum bootstrap is provably not tight in two dimensions, while the eigenstate bootstrap appears to remain tight in the tested settings.
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Bootstrapping periodic quantum systems
A bootstrap method that includes the translation operator and uses reality conditions computes accurate Bloch-band dispersion relations for the cosine potential without positivity constraints.
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