Physics – Quantum Physics
Scientific paper
1997-10-02
Physics
Quantum Physics
Latex, 21 pages, extended and slightly modified, new references added
Scientific paper
A nonlinear modification of the Schr\"{o}dinger equation is proposed in which the Lagrangian density for the Schr\"{o}dinger equation is extended by terms polynomial in $\Delta^{m}\ln (\Psi^{*}/{\Psi})$ multiplied by $\Psi^{*}{\Psi}$. This introduces a homogeneous nonlinearity in a Galilean invariant manner through the phase $S$ rather than the amplitude $R$ of the wave function $\Psi =R\exp (iS)$. From this general scheme we choose the simplest minimal model defined in some reasonable way. The model in question offers the simplest way to modify the Bohm formulation of quantum mechanics so as to allow a leading phase contribution to the quantum potential and a leading quantum contribution to the probability current removing asymmetries present in Bohm's original formulation. It preserves most of physically relevant properties of the Schr\"{o}dinger equation including stationary states of quantum-mechanical systems. It can be thought of as the simplest model of nonlinear quantum mechanics of extended objects among other such models that also emerge within the general scheme proposed. The extensions of this model to $n$ particles and the question of separability of compound systems are studied. It is noted that there exists a weakly separable extension in addition to a strongly separable one. The place of the general modification scheme in a broader spectrum of nonlinear modifications of the Schr\"{o}dinger equation is discussed. It is pointed out that the models it gives rise to have a unique definition of energy in that the field-theoretical energy functional coincides with the quantum-mechanical one. It is found that the Lagrangian for its simplest variant represents the Lagrangian for a restricted version of the Doebner-Goldin modification of this equation.
No associations
LandOfFree
Nonlinear Phase Modification of the Schroedinger Equation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Nonlinear Phase Modification of the Schroedinger Equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Nonlinear Phase Modification of the Schroedinger Equation will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-92735