WAVE FUNCTION TO PARTITION FUNCTION: A CORRELATION

JAYDIP DATTA

Published Mar 30, 2021• 1 citation

Abstract

In this note the statistical thermodynamics is correlated to wave function through mathematical probability. The note can be subdivided into two following portions.STATISTICS -THE BASIC OF STATISTICAL THERMODYNAMICS: A CORRELATION and PROBABILITY -A THE BASICS OF WAVE FUNCTION .Randomisation , Wave Function , Probability Density Function , Multiplicative Probability , Partition function , Correlation ( K.P ) coefficient , Probability , Weights , Stirling’s Approximation. Updated to Boltzmann -sigmoid function .

DOI: 10.31219/osf.io/m9dzb

Related papers

SOME COMMENTS ON STATISTICAL THERMODYNAMICS

R. Liljeblad

ABS>An attempt is made to correlate the classical Boltzmann, the Bose- Einstein, and the Fermi statistics. This is made pessible by modifying the presentation of the firstmentioned statistics. At the same time, a satisfactory reply is given to the criticism by Loschmidt and others of the inconsistency between the classical Boltzmann theory and the general laws of mechanics. It is pointed out that the customary usage of the term particle for something without identity for the image points in statistical thermodynamics is very misleading. It is suggested that such particles, i.e., image pcints, should be considered as singularities in a field. (auth)

Jan 1, 19590 citations

Density matrices and path integrals

Werner Krauth

Abstract In this chapter, we continue our parallel exploration of statistical and computational physics, but now move to the field of quantum mechanics, where the density matrix generalizes the classical Boltzmann distribution. The density matrix constructs the quantum statistical probabilities from their two origins: the quantum mechanical wave functions and the Boltzmann probabilities of the energy levels. The density matrix can thus be defined in terms of the complete solution of the quantum problem (wave functions, energies), but all this information is available only in simple examples, such as the free particle or the harmonic oscillator. A simple general expression exists for the density matrix only at high temperature.

Sep 14, 20060 citations

Basics of Quantum Mechanics

Normand M. Laurendeau

We found in the previous chapter that the molecular partition function is required to determine the thermodynamic properties of an ideal gas. To evaluate the partition function, specification of pertinent energy levels and degeneracies is necessary. Such knowledge demands that we investigate at least the rudiments of quantum mechanics, and especially those quantum concepts required for subsequent applications to statistical thermodynamics. For this reason, we concentrate in the next few chapters on the Schrödinger wave equation, whose various solutions provide the ε j 's and g j 's needed for the eventual calculation of thermodynamic properties. Depending on your academic background, you might thus consider reviewing classical mechanics (Appendix G) and operator theory (Appendix H) in preparation for your upcoming study of quantum mechanics. We begin this chapter with a historical review of the developments leading to the formulation of quantum mechanics, subsequently focusing on the Bohr model for atomic hydrogen and the de Broglie hypothesis for matter waves. We then introduce the Schrödinger wave equation, the basic postulates of quantum mechanics, and salient insights from these postulates germane to the development of statistical thermodynamics. We next apply the Schrödinger wave equation to the translation energy mode of an atom or molecule. This application conveniently explains both quantum states and quantum numbers, including their relation to our previous notions of microstate and macrostate. We end this chapter by discussing the Heisenberg uncertainty principle, including its utility in defining indistinguishability and symmetry conditions for multiparticle systems.

Cambridge University Press eBooksNov 21, 20052 citations

Quantum Statistical Mechanics Functional Integral Approach

Lukong Cornelius Fai

We establish a rather deep relation between statistical mechanics and quantum mechanics at an imaginary time. For the quantum field theory, this implies a relation between finite temperature quantum field theory in Minkowski space and quantum field theory in Euclidean space with one compact Euclidean time direction. The quantum mechanical language being a proper formulation of statistical physics as a molecular theory is basically the study of quantum equilibrium as well as non-equilibrium systems. A quantum system found in a thermodynamic equilibrium state with an external classical system (thermostat or thermal reservoir) may be characterized by fixed values of thermodynamic parameters of the system, say, for example, temperature T , volume V and number of particles N . In this way the total energy of the thermostat is assumed to be much greater than the energy of the system. The behavior of the quantum system may be assumed to be independent of the nature of the thermostat. The most convenient object of the quantum theory to describe such non-isolated systems is the density matrix since the partition function does not determine any local thermodynamic quantities. It is for this reason that we introduced quantum mechanical and quantum statistical density matrices which are necessary to do the investigation via path integration. This enables us to make a transition to the quasi-classical approximation of quantum statistical mechanics, which, in turn, enables us to evaluate the first quantum correction to the classical Boltzmann distribution function.

CRC Press eBooksFeb 19, 20210 citations

THERMO FIELD DYNAMICS AND PARA STATISTICAL MECHANICS

Sagarika Biswas, Ashok Das

Within the framework of thermo field dynamics, we derive the partition functions for a harmonic oscillator obeying parafermi and parabose statistics. The thermodynamic functions are studied for different limits of the order of the statistics and are shown to have the expected behaviour.

Modern Physics Letters AMay 1, 198810 citations

Quantum wave probability derive thermodynamic distribution

li xiao lin

Using the concept of quantum wave probability, combined with the identity principle, we can derive the Boltzmann distribution, Fermi distribution, and Bose distribution. Different distributions correspond to different conditions. The Boltzmann condition corresponds to the Boltzmann distribution. The Fermi condition corresponds to the Fermi distribution. The Bose condition corresponds to the Bose distribution. This demonstrates that the foundation of these three statistical distributions is quantum wave probability, all originating from quantum mechanics. The Boltzmann distribution is also an independent quantum distribution and is not simply a sparse limit of the Fermi or Bose distributions. The essence of the Boltzmann distribution is a uniform distribution. The Fermi and Bose distributions are deviations from the uniform distribution. Particles that follow the Boltzmann distribution can be called Boltzmannons. Boltzmann entropy based on the quantum wave probability can resolve the Gibbs paradox. We need to rethink the fundamentals of statistical mechanics.

Nov 6, 20250 citations