Non-standard Lagrangians in Quantum Mechanics and Their Relationship with Attosecond Laser Pulse Formalism

Lately, the notion of non-standard Lagrangians or non-natural Lagrangians was discussed extensively in literature in an attempt to explore some basic problems of theory of non-linear differential equations: in fact, non-standard Lagrangians came in different mathematical forms depending on the dynamical problems under study. Exponential Lagrangians are motivating since they have revealed a number of nice properties at both classical and quantum levels. In this paper we will discuss some of their implications in quantum mechanics where some new dynamical properties are obtained. It is proved that several constrained Lagrangians possess some interesting features similar to the ones obtained by in the previous work of Marciak-Kozlowska and Kozlowski, which describe the interaction of electrons with their surroundings in the atom and detected with the attosecond laser pulse.