Relativistic Levinson theorem in two dimensions
Abstract
In the light of the generalized SturmLiouville theorem, the Levinson theorem for the Dirac equation in two dimensions is established as a relation between the total number n_{j} of the bound states and the sum of the phase shifts η_{j}(+/M) of the scattering states with the angular momentum j: η_{j}(M)+η_{j}(M)=(n_{j}+1)πwhen a half bound state occurs at E=M and j=3/2 or  1/2(n_{j}+1)πwhen a half bound state occurs at E=M and j=1/2 or  3/2n_{j}π the remaining cases.The critical case, where the Dirac equation has a finite zeromomentum solution, is analyzed in detail. A zeromomentum solution is called a halfbound state if its wave function is finite but does not decay fast enough at infinity to be square integrable.
 Publication:

Physical Review A
 Pub Date:
 September 1998
 DOI:
 10.1103/PhysRevA.58.2160
 arXiv:
 arXiv:quantph/9806006
 Bibcode:
 1998PhRvA..58.2160D
 Keywords:

 03.80.+r;
 03.65.Ge;
 11.80.m;
 73.50.Bk;
 Solutions of wave equations: bound states;
 Relativistic scattering theory;
 General theory scattering mechanisms;
 Quantum Physics
 EPrint:
 Latex 14 pages, no figure, submitted to Phys.Rev.A