ANALYTIC PROPERTIES OF THE QUANTUM CORRECTIONS TO THE SECOND VIRIAL COEFFICIENT

Journal Article · Mon Jan 01 04:00:00 EST 1962 · J. Math. Phys.

DOI:https://doi.org/10.1063/1.1724287· OSTI ID:4782230

DeWitt, H. E.

The use of the perturbation expansion and the WignerKirkwood exparnsion of the quantum-mechanical partition function is discussed for various interaction potentials. It is shown that, contrary to what is expected from the Wigner- Kirkwood expansion, quantum-mechanical diffraction corrections at high temperature to the classicali partition function may involve nonanalytic forms of h/sub 2/. This can occur when the second-order perturbation term is finite in the classical limit, and the interaction potential has a cusp or singularity in any derivative. The second-order perturbation term is evaluated exactly for the exponential, screened Coulomb, and square barrier potentials, and the nonanaliytic form (h/sup 2/)/sup 1/2/ is found. For potentials more singular than 1/r at the origin, the diffraction corrections are analytic in h/sup 2/. A method of deriving the Wigner-Kirkwood expansion from the perturbation expansion is given. The method allows the subtraction of any order of the perturbation expansion that can be evaluated separately, and is particularly useful for the screened Coulomb potential. The classical second virial coefficient and the O(h/ sup 2/) and O(h/sup 4/) diffraction corrections are evaliuated for the singular potential, u(r) = (g/sub p//r/sup p/)e/sup -r/r/sub 0/, by using the MeIIin tran sform of e/sup -Bu/. (auth)

• Research Organization: Univ. of California, Livermore
• NSA Number: NSA-17-002448
• OSTI ID: 4782230
• Report Number(s): UCRL-6611
• Journal Information: J. Math. Phys., Journal Name: J. Math. Phys. Vol. Vol: 3
• Country of Publication: United States
• Language: English

Related Subjects

DIFFRACTION
ELECTRIC POTENTIAL
ERRORS
GASES
INTERACTIONS
MATHEMATICS
PERTURBATION THEORY
PHYSICS
QUANTUM MECHANICS
SINGULARITY
TEMPERATURE
THERMODYNAMICS
VIRIAL COEFFICIENTS