A Small Note on The 'Density Matrix'

The whole game of Quantum Mechanics is about finding out the probability! On the other hand, Statistical Mechanics may be put on the equal foot, although the context is a littile different. But, both the cases, deal with probabilistic approach(Atleast to the Born Oppenheimer interpretation). Whenever these two high-achiever intertwine, something beautiful happen. We get all sort of useful results as the by product. And an interesting quantity appear, known as ‘Density Matrix’. Perhaps it is possible to study Quantum mechanical systems statistically without introducing Density Matrix, nevertheless, it simplifies many thing and it is rich in concept.

Lagrangian Dynamics of Kapitza's Pendulum and It's Numerical Solution

Kapitza’s Pendulum is nothing but a regular pendulum which is inverted and pivoted to a oscillator. Interestingly, When the frequency of the oscillator is very high, the pendulum doesn’t fall down. Here we seek for the equation of motion and numerical solution for such system.