Levinson's theorem for the Klein-Gordon equation

Journal Article · Tue Jul 15 04:00:00 EDT 1986 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.34.565· OSTI ID:5521014

Liang, Y; Ma, Z

Levinson's theorem is generalized to relativistic scalar particles satisfying the Klein-Gordon equation with a spherically symmetric potential V-italic(r-italic), which is the fourth component of a vector field, and shown to be N-italic/sub l-italic/ = n/sub l//sup (+)/-n/sub l//sup (-)/ = (1/ ..pi..)(delta/sub l/(M)+..cap alpha../sub 1/)-(1/..pi..)(delta/sub l/ (-M)+..cap alpha../sub 2/), where N-italic/sub l-italic/ denotes the difference of the numbers of the particle bound states and the antiparticle ones with a definite angular momentum l-italic, delta/sub l-italic/(E) is the phase shift, and ..cap alpha../sub 1/ and ..cap alpha../sub 2/ are constants reflecting the critical cases where bound states or half bound states occur at E-italic = +- M-italic.

• Research Organization: Department of Physics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061
• OSTI ID: 5521014
• Journal Information: Phys. Rev. D; (United States), Journal Name: Phys. Rev. D; (United States) Vol. 34:2; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
657002 -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANGULAR MOMENTUM
BOUND STATE
DIFFERENTIAL EQUATIONS
ENERGY RANGE
EQUATIONS
KLEIN-GORDON EQUATION
LEVINSON THEOREM
PARTIAL DIFFERENTIAL EQUATIONS
PHASE SHIFT
RELATIVISTIC RANGE
VECTOR FIELDS
WAVE EQUATIONS