Lecturer: Kenji Yajima
(Tokyo Gakushuin) venue and schedule: Monday 14:3016:00 A136  Wednesday 14:3016:00 A134 start: Friday 6 May 2016, 11:15, A136 end: Wednesday 29 June 2016 duration: 40 hours (2 cycles) Topics: 1. Free Schrödinger equation. 1.1. Free propagator, MDFMformula,
2. Free Schrödinger operators1.2. Large time behavior, Asymptotic expansion 1.3. LpLq estimates, Strichartz’ estimate I 1.4. Strichartz’ estimate II 1.5. Application of Strichartz’ estimates to NLSE
2.1. Spectral decomposition I
3. Selfadjointness2.2. Spectral decomposition II 2.3. Limitting absorption principle (LAP) 2.4. Kato smoothness and local smoothing property 2.5. Resolvent kernel
3.1. KatoRellich theorem and selfadjointness of electronic systems.
4. Onebody scattering theory3.2. Kato’s inequality and positive potentials. 3.3. Quadratic forms and Kato potentials 3.4. Diamagnetic inequality 3.5. LeinfelderSimader’s theorem 3.6. Essential spectrum and discrete spectrum
4.1. RAGE theorem
4.2. Existence of wave operators 4.3. Asymptotic completeness 4.4. Proof via Enss method 4.5. Stationary scattering theory a. Limitting absorption principle, proof by AgmonKuroda
b. Mourre theory and proof of LAP by Mourre theorem c. Proof of asymptotic completeness via LAP d. Eigenfunction expansions via scatterin solutions e. Wave operators as transplantations f. Scattering amplitute and scattering matrix Prerequisites: a general knowledge at the undegrad level of:
Literature: discussed in class 

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