Notes Freely falling particle using the H-J method To determine the motion of a particle falling vertically in a uniform gravitational field, the Hamiltonian is given byH = T + V = p²/ 2m + mgy .........1...
Notes Small oscillations Lagrangian approach is suitable for the system with small oscillation about an equilibrium position. The theory of small oscillation about equilibrium position is applicable in molecular spectra, …
Notes Introduction to continuous systems and fields Certain mechanical issues require a continuous system. For instance, consider the issue of an elastic solid that is vibrating. Here, the oscillation is caused by each point of the continuous ...
Notes Entropy of a classical ideal gas using the concept of microcanonical ensemble The microcanonical ensemble describes a system that is isolated and has a fixed total energy. For an ideal gas, the total energy of the system is the sum of the ...
Notes Gibb's paradox and its resolution Gibbs' paradox is a problem in statistical mechanics that arises when attempting to calculate the entropy of a mixture of two ideal gases. The paradox is that the entropy of ...
Notes Langevin's theory of Paramagnetism Consider a system of N atoms each of which has magnetic moment of magnitude μ. The Hamiltonian in presence of external magnetic field (B) isH (p,q) - μB Σ ...
Notes Theorem of equipartition of energy (Boltzman equipartition) From generalized equipartition theorem< xi, ∂H/∂xj > = ðij KBT...................1Many physical system have Hamiltonian which in classical transformation can be expressed aswhere Ai and Bi are …
Notes Polarisability per molecule in terms of Langevin's function In polar substance, the permanent dipoles are random oriented due to the thermal agitation. So the net dipole moment is zero. When an external field is applied, the dipoles align ...
