To acquire a good knowledge of the elementary theory of partial differential equations and of the basic methods of solution, with particular focus on the equations describing problems in mathematical physics.
scheda docente
materiale didattico
[Cr] W. Craig, A course on Partial Differential Equations
[L1] V. Lubicz, Apppunti di Meccanica Quantistica
Programma
Evolution equations of Mathematical Physics: transport, wave and heat equations. Introduction to quantum mechanics. Fourier transformTesti Adottati
[B] P. Butta', Note del corso di Fisica Matematica[Cr] W. Craig, A course on Partial Differential Equations
[L1] V. Lubicz, Apppunti di Meccanica Quantistica
Bibliografia Di Riferimento
[B] A. Bohm, Quantum Mechanics - Foundations and Applications [Co] M. Correggi, Aspetti Matematici della Meccanica Quantistica [T] L. Takhtajan, Quantum Mechanics for MathematiciansModalità Erogazione
Classes will be held regularly on campus. However they will also be available online and recorded.Modalità Frequenza
Attendance is not mandatory but strongly suggestedModalità Valutazione
The exam consists in a written test, possibily split into two midterms, and in an oral exam in which the student will discuss the material presented in class
scheda docente
materiale didattico
Programma
Introduction to the study of partial derivative equations in mathematical physics. Wave equation: transport; wavefront; conservation laws; Duhamel's principle. Heat equation: heat core; maximum principle; entropy. Introduction to quantum mechanics: historical background, free Schroedinger equation, Stern-Garlach experiment, postulates of quantum mechanics, properties of Hilbert spaces, harmonic oscillator, hydrogen atom.