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We present a nonrelativistic wave equation for the electron in (3+1)-dimensions which includes negative-energy eigenstates. We solve this equation for three well-known instances, reobtaining the corresponding Pauli equation (but including negative-energy eigenstates) in each case.
Lagrangian formulation of quantum mechanical Schrodinger equation is developed in general and illustrated in the eigenbasis of the Hamiltonian and in the coordinate representation. The Lagrangian formulation of physically plausible quantum system res
This paper presents a detailed Lyapunov-based theory to control and stabilize continuously-measured quantum systems, which are driven by Stochastic Schrodinger Equation (SSE). Initially, equivalent classes of states of a quantum system are defined an
We show that the Schr{o}dinger-Newton equation, which describes the nonlinear time evolution of self-gravitating quantum matter, can be made compatible with the no-signaling requirement by elevating it to a stochastic differential equation. In the de
Utilization of a quantum system whose time-development is described by the nonlinear Schrodinger equation in the transformation of qubits would make it possible to construct quantum algorithms which would be useful in a large class of problems. An ex
We present a detailed account of a first-order localization transition in the Discrete Nonlinear Schrodinger Equation, where the localized phase is associated to the high energy region in parameter space. We show that, due to ensemble inequivalence,