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J. Conway Spirited Seminar Series: Variational Principles in Mathematical Physics: From Semibounded to Gapped Operators

J. Conway Spirited Seminar Series: Variational Principles in Mathematical Physics: From Semibounded to Gapped Operators

Attend the J. Conway Spirited Seminar Series on 'Variational Principles in Mathematical Physics: From Semibounded to Gapped Operators' with Dr. Lukas Schimmer (Institut Mittag-Leer, Royal Swedish Academy of Sciences).

October 4, 2021

Time:

4:00 pm

Online

For a semibounded, self-adjoint operator the eigenvalues below the essential spectrum can be computed in terms of the well-known min-max principle. This variational principle takes a particularly simple form for the Friedrichs extension of a semibounded, symmetric operator. The prime application concerns the Schrödinger operator in non-relativistic quantum mechanics where the principle does not only provide a way to numerically compute the bound states but is also a key ingredient in the proof of many important spectral bounds relating to the stability of matter.

This talk will begin with an introduction to this min-max principle, and then subsequently present a generalisation of the principle to the setting of self-adjoint operators satisfying only a gap condition. Again, the principle takes a particularly simple form for a certain distinguished self-adjoint extension. The results apply to the Dirac operator in relativistic quantum mechanics. This talk is partly based on joint work with Jan Philip Solovej and SabihaTokus.

Date: Monday, October 4, 2021
Time: 4:00 pm
Link: https://zoom.us/j/97379855766
Meeting ID: 973 7985 5766
Passcode: 146928

Add to Calendar 2021-10-04 16:00:00 2021-10-04 17:00:00 J. Conway Spirited Seminar Series: Variational Principles in Mathematical Physics: From Semibounded to Gapped Operators For a semibounded, self-adjoint operator the eigenvalues below the essential spectrum can be computed in terms of the well-known min-max principle. This variational principle takes a particularly simple form for the Friedrichs extension of a semibounded, symmetric operator. The prime application concerns the Schrödinger operator in non-relativistic quantum mechanics where the principle does not only provide a way to numerically compute the bound states but is also a key ingredient in the proof of many important spectral bounds relating to the stability of matter. This talk will begin with an introduction to this min-max principle, and then subsequently present a generalisation of the principle to the setting of self-adjoint operators satisfying only a gap condition. Again, the principle takes a particularly simple form for a certain distinguished self-adjoint extension. The results apply to the Dirac operator in relativistic quantum mechanics. This talk is partly based on joint work with Jan Philip Solovej and SabihaTokus. Date: Monday, October 4, 2021 Time: 4:00 pm Link: https://zoom.us/j/97379855766 Meeting ID: 973 7985 5766 Passcode: 146928 Online LUMS Drupal 8 adil.sarwar@lums.edu.pk Asia/Karachi public

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J. Conway Spirited Seminar Series: Variational Principles in Mathematical Physics: From Semibounded to Gapped Operators

J. Conway Spirited Seminar Series: Variational Principles in Mathematical Physics: From Semibounded to Gapped Operators

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