Notes Comparison of classical and quantum probability density of harmonic oscillator The comparison between classical and quantum probability density of a harmonic oscillator highlights some fundamental differences between classical mechanics and quantum mechanics. The harmonic …

Notes Dirac correspondence principle The Dirac correspondence principle, also known as Dirac's theorem, is a fundamental concept in the bridge between quantum mechanics and classical mechanics. It describes how the quantum mechanical …

Notes Legrendre Transformation In Lagrangian formulation,The partial derivative of L with respect to qi means a derivative taken with all q's and q̇ 's constant. But in Hamilton's principle (Hamilton's approach) q's ...

Notes Kepler's problem by H-J method Kepler's problem is basically a problem related to central force. For simplicity we take inverse square force between nucleus of charge 'Ze' and electron of charge 'e'. One of the ...

Notes Poisson Bracket ELI5: Imagine you have a big toy box filled with different toys like cars, dolls, action figures, etc. Each toy represents a different thing, like the position and speed of ...

Notes Poisson's Second Theorem Statement: '' The poisson bracket of two constant of motion is itself a constant of motion.''If u and v are constant of motions then their poisson's bracket is also ...

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 Free vibrations of a linear triatomic molecule Fig: Model of a linear symmetric triatomicLet us consider two atoms of mass m are symmetric triatomic located on each side of an atom of mass M. All three ...