Physics – Quantum Physics
Scientific paper
2006-07-31
J.Phys.A40:5621-5636,2007
Physics
Quantum Physics
Final Journal Version; 23 pages inclusive of 3 figures
Scientific paper
10.1088/1751-8113/40/21/012
Using perturbative methods, we analyse a nonlinear generalisation of Schrodinger's equation that had previously been obtained through information-theoretic arguments. We obtain analytical expressions for the leading correction, in terms of the nonlinearity scale, to the energy eigenvalues of the linear Schrodinger equation in the presence of an external potential and observe some generic features. In one space dimension these are: (i) For nodeless ground states, the energy shifts are subleading in the nonlinearity parameter compared to the shifts for the excited states, (ii) the shifts for the excited states are due predominantly to contribution from the nodes of the unperturbed wavefunctions and (iii) the energy shifts for excited states are positive for small values of a regulating parameter and negative at large values, vanishing at a universal critical value that is not manifest in the equation. Some of these features hold true for higher dimensional problems. We also study two exactly solved nonlinear Schrodinger equations so as to contrast our observations. Finally, we comment on the possible significance of our results if the nonlinearity is physically realised.
Parwani Rajesh R.
Tabia Gelo
No associations
LandOfFree
Universality in an Information-theoretic Motivated Nonlinear Schrodinger 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 Universality in an Information-theoretic Motivated Nonlinear Schrodinger Equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Universality in an Information-theoretic Motivated Nonlinear Schrodinger Equation will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-33662