On Dielectric Constants and Magnetic Susceptibilities in the new Quantum Mechanics Part I. A General Proof of the Langevin-Debye Formula

摘要: In contradistinction to the old quantum theory, new mechanics yields very generally Langevin and Debye formulas $\ensuremath{\chi}=N\ensuremath{\alpha}+\frac{N{\ensuremath{\mu}}^{2}}{3kT}$ for magnetic dielectric susceptibilities respectively. It is believed that our proof considerably more comprehensive than previous ones, it assumes only atom or molecule has a "permanent" vector moment of constant magnitude $\ensuremath{\mu}$ whose precession frequencies are small compared $\frac{\mathrm{kT}}{h}$. There no limit allowable number superposed precessions. can, instance, be simultaneous precessions due internal spins electron "temperature rotation" nuclei. The presence other external fields in addition applied electric field introduces difficulty. Besides effect permanent moment, there term $N\ensuremath{\alpha}$ which arises from "high frequency" matrix elements associated with transitions normal excited states. This proved independent temperature. susceptibility formula contains factor $\frac{1}{3}$ temperature as classical theory because high spectroscopic stability characteristic mechanics. shown mean squares $x$, $y$, $z$ components equal dynamics just difference being we take average by summing over discrete distribution quantum-allowed orientations instead integrating uniform continuous distribution.