Applications of a metaplectic calculus to Schrödinger evolutions with non-self-adjoint generators

Joe Viola
2018 Journées Équations aux dérivées partielles  
Applications of a metaplectic calculus to Schrödinger evolutions with non-self-adjoint generators Abstract We review the calculus of metaplectic operators and shifts in phase space applied to Gaussian wave packets. Using holomorphic extensions of this calculus, one can reduce the L 2 theory of evolution equations with non-selfadjoint quadratic generators to symplectic linear algebra. We illustrate these methods through an application to the quantum harmonic oscillator with complex perturbation ix.
more » ... mplex perturbation ix.
doi:10.5802/jedp.671 fatcat:5zooyb6jnje3jhgqmect3nlv6q