Pseudo-Classical Partition Function of Spin One-Half Derived by Coherent State Method

2010 ◽  
Vol 53 (6) ◽  
pp. 1046-1048
Author(s):  
Xu Ye-Jun ◽  
Fan Hong-Yi
Keyword(s):  
Partition Function ◽  
Coherent State ◽  
State Method ◽  
Classical Partition Function

A REMARK ON PRIME DIVISORS OF PARTITION FUNCTIONS

2014 ◽  
Vol 10 (01) ◽  
pp. 125-131
Author(s):  
PAUL POLLACK
Keyword(s):  
Partition Function ◽  
Wide Class ◽  
Analogous Result ◽  
Partition Functions ◽  
Prime Divisors ◽  
Classical Partition Function

Schinzel showed that the set of primes that divide some value of the classical partition function is infinite. For a wide class of sets 𝒜, we prove an analogous result for the function p𝒜(n) that counts partitions of n into terms belonging to 𝒜.

Thermodynamic Functions of Pendular Molecules

1993 ◽  
Vol 58 (10) ◽  
pp. 2458-2473 ◽  
Author(s):  
Břetislav Friedrich ◽  
Dudley R. Herschbach
Keyword(s):  
Partition Function ◽  
Thermodynamic Functions ◽  
Energy Levels ◽  
Quantum Statistical Mechanics ◽  
Rotational Constant ◽  
Chemical Equilibria ◽  
Rotational States ◽  
Dipolar Molecules ◽  
Linear Molecules ◽  
Classical Partition Function

External electric or magnetic fields can hybridize rotational states of individual dipolar molecules and thus create pendular states whose field-dependent eigenproperties differ qualitatively from those of a rotor or an oscilator. The pendular eigenfunctions are directional, so the molecular axis id oriented. Here we use quantum statistical mechanics to evaluate ensamble properties of the pendular states. For linear molecules, the partition function and the averages that determine the thermodynamic functions can be specified by two reduced variables involving the dipole moment, field strength, rotational constant, and temperature. We examine a simple approximation due to Pitzer that employs the classical partition function with quantum corrections. This provides explicit analytic formulas which permit thermodynamic properties to be evaluated to good accuracy without computing energy levels. As applications we evaluate the high-field average orientation of the molecular dipoles and field-induced shifts of chemical equilibria.

Sign in / Sign up

Export Citation Format

Share Document