• Corpus ID: 232076545

Generalized Continuity Equations for Schr\"odinger and Dirac Equations

  title={Generalized Continuity Equations for Schr\"odinger and Dirac Equations},
  author={Angelos Katsaris and Panayotis A. Kalozoumis and Fotis K. Diakonos},
The concept of the generalized continuity equation (GCE) was recently introduced in [J. Phys. A: Math. and Theor. 52, 1552034 (2019)], and was derived in the context of N independent Schrödinger systems. The GCE is induced by a symmetry transformation which mixes the states of these systems, even though the N -system Lagrangian does not. As the N -system Schrödinger Lagrangian is not invariant under such a transformation, the GCE will involve source terms which, under certain conditions vanish… 

Figures from this paper


Generalized continuity equations from two-field Schrödinger Lagrangians
A variational scheme for the derivation of generalized, symmetry-induced continuity equations for Hermitian and non-Hermitian quantum mechanical systems is developed. We introduce a Lagrangian which
Low momentum scattering in the Dirac equation
It is shown that the amplitude for reflection of a Dirac particle with arbitrarily low momentum incident on a potential of finite range is −1 and hence the transmission coefficient T = 0 in general.
Super-Lagrangian and variational principle for generalized continuity equations
We present a variational approach which shows that the wave functions belonging to quantum systems in different potential landscapes, are pairwise linked to each other through a generalized
  • Rev. B 92, 014303
  • 2015
  • Rev. A 88, 033857
  • 2013
  • Rev. A 87, 032113
  • 2013
Invariante Variationsprobleme
  • Nachr. D. König. Gesellsch. D. Wiss. Zu Göttingen, Math-phys. Klasse 1918: 235–25
  • 1918