The Schrödinger equation forms the basic principles of quantum mechanics (like that of Newton’s second law in classical mechanics). It also plays an important role in describing waves at an appropriate regime in classical fluid dynamics (e.g., water waves) and plasma physics (e.g., Langmuir’s waves or oscillations in a plasma!). In this quick note, I shall present a few basic properties and classical results for the Schrödinger equations, focusing mainly on the defocusing cubic nonlinear equations
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