M Gadella et al 2009 J. Phys. A: Math. Theor. 42 465207 doi:10.1088/1751-8113/42/46/465207
A delta well with a mass jump
M Gadella, F J H Heras, J Negro and L M Nieto
Show affiliationsIn this paper, it is shown that a one-dimensional Hamiltonian with an attractive delta potential at the origin plus a mass jump at the same point cannot have a bound state, as is the case with the ordinary attractive delta potential with constant mass, unless another term is added into the potential in the form of a derivative of the Dirac delta at the origin. The consistency of this singular potential with two terms is guaranteed by choosing suitable matching conditions at the singular point for the wavefunctions. Furthermore, it is proved that the self-adjointness of the Hamiltonian with both singular interactions determines the coefficient of the derivative of the delta in a unique manner. Under these conditions, the bound state and its energy are obtained and it is checked that the correct results in the limit of equal masses are obtained.
- PACS
-
03.65.Ge Solutions of wave equations: bound states
- MSC
- Subjects
- Dates
-
Issue 46 (20 November 2009)
Received 30 May 2009, in final form 28 August 2009
Published 26 October 2009
-
A delta well with a mass jump
M Gadella et al 2009 J. Phys. A: Math. Theor. 42 465207
-
Regularization in Hilbert space under unbounded operators and general source conditions
Bernd Hofmann et al 2009 Inverse Problems 25 115013
-
Selective tumor imaging by a novel tumor specific aralin-infrared-to-visible phosphor conjugate
Y Kawasaki et al 2009 J. Phys.: Conf. Ser. 191 012001
-
Design of Double Cladding Nearly Zero Dispersion Flattened Nonlinear Photonic Crystal Fiber
Wang Wei et al 2009 Chinese Phys. Lett. 26 114205
-
Classification of sideband instability regimes for whistler waves with trapped electrons
V L Krasovsky 2009 Plasma Phys. Control. Fusion 51 115011
-
Characterization of the transient thermal-lens effect using top-hat beam Z-scan
Junyi Yang et al 2009 J. Phys. B: At. Mol. Opt. Phys. 42 225404
-
Current flow mechanism in Cu2O/p-Si heterojunction prepared by chemical method
T Serin et al 2009 J. Phys. D: Appl. Phys. 42 225108
-
Non-diagonal reflection for the non-critical XXZ model
Anastasia Doikou 2008 J. Phys. A: Math. Theor. 41 194007
-
Dynamically slow processes in supercooled water confined between hydrophobic plates
Giancarlo Franzese and Francisco de los Santos 2009 J. Phys.: Condens. Matter 21 504107
-
Influence of wall roughness on the geometrical, mechanical and transport properties of single fractures
H Auradou 2009 J. Phys. D: Appl. Phys. 42 214015
Users also read
What's this?- On the generation of anomalous diffusion
- Parity-odd effects and polarization rotation in graphene
- Algebraic characterization of X-states in quantum information
supergravity chiral projection operatorRelated review articles
What's this?- Integrable structure of box–ball systems: crystal, Bethe ansatz, ultradiscretization and tropical geometry
- Lectures on localization and matrix models in supersymmetric Chern–Simons-matter theories
- Exact superconformal and Yangian symmetry of scattering amplitudes