A PROBLEM IN THERMODYNAMICS AND STATISTICAL MECHANICS: ANALYTICAL AND NUMERICAL STUDY OF AN EINSTEIN SOLID-Analytical Solution

IMAGE CREDIT/OBTAINED FROM:  https://mappingignorance.org/2015/12/17/einstein-and-quantum-solids/ Quite some time ago, I had posted a numerical study of an Einstein solid and I now present the analytical study of an Einstein solid. As this was one problem in one of my problem sets while studying thermodynamics and statistical mechanics, one may find this exact problem in the following text: […]

Basics of Tensor Calculus and General Relativity: An Introduction to Manifolds and Coordinates

SOURCE FOR CONTENT: General Relativity: An Introduction for Physicists, Hobson, M.P., Efsttathiou, G., and Lasenby, A.N., 2006. Cambridge University Press.  D-Dimensional Hypersphere and Gamma Function: Introduction to Thermal Physics, Schroeder D.V. 2000. Addison-Wesley-Longmann.  IMAGE CREDIT: NASA/JPL.  The intended purpose of the post is to introduce the concept of manifolds in the context of physics (mathematicians beware!). Furthermore, […]

Derivation of the Euler-Lagrange Equation for a Function of Several Dependent Variables

IMAGE CREDIT: NASA/JPL SOURCE FOR CONTENT: Classical Dynamics of Particles and Systems. Thornton and Marion. 5th Edition.    Consider a functional where . By the method used in a previous section of the aforementioned text, we may write Additionally, we will find it useful to define Further we may also define an integral functional by way of […]