Recent content by dd331

  1. D

    Graduate Paramagnetic term of the hamiltonian

    The Hamiltonian for particle in an EM field is H = 1/2m (p - qA)^2 + q phi If we take the cross-terms, which corresponds to the paramagnetic term, we have H para = -q/2m * (p.A + A.p ) = iqh/2m * (\nabla .A + A.\nabla) What I do not understand is how this simplifies...
  2. D

    Graduate Why use a Legendre transform instead of a simple change of variable?

    I think you will find this useful http://www2.ph.ed.ac.uk/~martin/sp/LT070902.pdf
  3. D

    Graduate Why are probabilities distribution of thermodynamic variables tend to Gaussian?

    The probability distribution for some thermodynamic variable x is given by P = N e^{-A(x)/KT} where A(x) is the availability, which can be replaced by Hemlholtz free energy F, Gibb's free energy G, etc depending on the conditions imposed. N is just some normalization constant. A(x) can be...
    • dd331
    • Thread
    • Distribution Gaussian Probabilities Thermodynamic Variables
    • Replies: 1
    • Forum: Thermodynamics
  4. D

    Graduate Physical meanings of universal coordinates in schwarzschild metric

    The metric due to the gravitational field of a spherical mass is described by the schwarzschild metric ds2 = c2 (1 - R/r) dt2 - (1 - R/r)-1 dr2 - r2 d\Omega 2 Where \Omega is the solid angle, and R is the schwarzschild radius. What are the physical meanings of the coordinates t and r...