We study operators theory in Hilbert spaces and its application to quantum mechanics. In lectures in the third year or fourth year in bachelor's course, there is usually not enough time to treat unbounded operators such as differential operators due to a lack of time. In this course we aim to study how to treat unbounded operators in Hilbert spaces and its application to quantum mechanics with concrete applications. There is an extention of the theory to Banach spaces and the theory constitutes the basis of the treatment of partial differential equations such as heat equation, wave equation and Schrodinger equation in appropriate Hilbert spaces. This study would form a basis of future study of Analysis.
We aim to master a functional analytic treatment of unbounded operators such as differential operators and its application to quantum mechanics with concrete examples.
