Variational methods for schrödinger type equations

It is well known that the Schrödinger equation is one of the most important equations in physics. It was formulated by E. Schrödinger in 1925 (which later in 1933 received the Nobel Prize in Physics) and introduced by taking into account the de Broglie hypothesis according to which matter particles possess a wave packet delocalized in space. According to the Copenhagen interpretation the square modulus of the wave function σ: R³ × R → C encloses the physical information on the particle; in particular, |σ|² is related to the probability of finding the particle in a specific space region. Since its formulation the Schrödinger equation is the object of many research from a physical and mathematical point of view.