Lagrangian Densities and Principle of Least Action in Nonrelativistic Quantum Mechanics

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dc.creatorKobe, Donald H.
dc.date2007-12-10
dc.date.accessioned2026-07-07T08:48:31Z
dc.date.available2026-07-07T08:48:31Z
dc.descriptionThe 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.
dc.description17 pages, no figures
dc.identifierhttps://arxiv.org/abs/0712.1608
dc.identifierhttp://arxiv.org/abs/0712.1608
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/143971
dc.subjectQuantum Physics
dc.titleLagrangian Densities and Principle of Least Action in Nonrelativistic Quantum Mechanics
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