  The Principle of Least Action is used with a simple Lagrangian density,
involving second-order derivatives of the wave function, to obtain the
Schroedinger equation. A Hamiltonian density obtained from this simple
Lagrangian density shows that Hamilton's equations also give the Schroedinger
equation. This simple Lagrangian density is equivalent to a standard Lagrangian
density with first-order derivatives. For a time-independent system the
Principle of Least Action reduces to the energy variational principle. For
time-dependent systems the Principle of Least Action gives time-dependent
approximations. Using a Hartree product trial wave function for a
time-dependent many-boson system, we apply the Principle of Least Action to
obtain the Gross-Pitaevskii equation that describes a Bose-Einstein condensate.
