Hi I'm currently learning Hamiltonian and Lagrangian Mechanics (which I think also encompasses the calculus of variations) and I've also grown interested in functional analysis. I'm wondering if there is any connection between functional analysis and Hamiltonian/ Lagrangian mechanics? Is there a connection between functional analysis and calculus of variations? What is the relationship between functional analysis and quantum mechanics; I hear that that functional analysis is developed in part by the need for better understanding of quantum mechanics?