Periodic Path Integral Measure

Turning to the Matsubara harmonic partition function algorithm (2.28)-(2.34) one successively has (Putz, 2009)  

Quantum Nanochemistry—Volume II Quantum Atoms and Periodicity 

Releasing the Matsubara partition function for the harmonic motion by replacing function (2.50) into expression (2.28)  

Comparing the form (2.51) with the consecrated result for harmonic oscilators partition function (see Volume I/Chapter 4 of the present five-volume book) one remains with the condition  

Choosing for the Feynman centroid integral the normalization factor that regains the inverse of the thermal length (280)  

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The ray-path parameters are calculated with reference to Fig. 1-9 which shows a bound-ray path between successive turning points P and Q, separated by the ray half-period Zp measured along the axis. The path length Lp and the optical path length Lg are defined by path integrals... 

With these atomizers, the free atoms are swept through the light path in a very brief period of time. Short, sharp peaks are frequently recorded and the peak heights are usually measured. Recent commercial equipment in which the peak area is integrated is more accurate because peak areas correspond more to the total number of atoms than to the maximum number of atoms produced. A problem frequently arises with coupling a furnace atomizer to equipment purchased for flame atomizers. The latter equipment usually utilizes amplifiers and readout systems with slow response times which are totally unsuitable for use with furnace atomizers. Such equipment can give answers which are more a measure of response time than of metal concentration. 

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