Mass dependence of Schroedinger wavefunctions

Journal Article · Sun Jul 01 04:00:00 EDT 1979 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.524226· OSTI ID:6246637

Leung, C N; Rosner, J

It is shown that for nonrelativistic central potentials of specific forms, the bound state wavefunctions u (r) have the property that G (r) equivalent..integral.. /sup r//sub 0/dx u (x)(partialu (x)/partial..mu..) > or =0 for all r. Here ..mu.. is the reduced mass. Thus, for such potentials, the probability that a particle lies within a spherical shell of radius r is a monotonically increasing function of ..mu... The forms for which this property has been established are (a) V (r) =Cr/sup epsilon/, -20 for nodeless states. It is shown explicitly that G (r) cannot be nonnegative for all bound states in an arbitrary monotonically increasing potential. The question remains open regarding the widest class of potentials for which G (r) is nonnegative for all bound states.

• Research Organization: School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455
• OSTI ID: 6246637
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 20:7; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOUND STATE
CENTRAL POTENTIAL
DIFFERENTIAL EQUATIONS
EQUATIONS
FUNCTIONS
PARTIAL WAVES
POTENTIALS
S WAVES
SCHROEDINGER EQUATION
WAVE EQUATIONS
WAVE FUNCTIONS