Density Function Thermal Scaling and Physical Significance of Shape Functions

Authors:

Carbó-Dorca R*

DOI: 10.23880/psbj-16000102

Volume 1, Issue 1

Abstract

The solid-state concept of thermal voltage is used to define a homothetic scaling of the quantum mechanical one-particle reduced density function. This scaling might be used to construct a temperature dependent quantum density. Once defined such scaling, named here as thermal scaling, it is simple to use it with a precise temperature, adapting such scaling matching the associated shape function. The temperature achieving this equality is termed Shape Temperature S T and, if N is the number of particles of a given quantum object, one can demonstrate that the simple equality: TS 12N holds. Furthermore, Shape Temperature can be associated to a characteristic Shape Frequency max S  , via Wien’s law, which yields equality: max 0.7 , S   N THz linking number of particles with frequency.

Keywords:

Electronic Density Function; Shape Function; Thermal Voltage; Density Function Scaling; Thermal Scaling; Shape Temperature; Shape Frequency

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