Quantum mechanics is a branch of physics which deals with physical phenomena at microscopic scales, where the action is on the order of the Planck constant.
Action : It is defined in the classical physics by time integration Lagrangian L = (T - V) of a system.
where T is the kinetic-energy and V is potential energy of the system.
![\mathcal{S}[\mathbf{q}(t)] = \int_{t_1}^{t_2} L[\mathbf{q}(t),\dot{\mathbf{q}}(t),t]\, dt](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_sL-6pDiKkmpELoowlIJwvm13-2elrsiBm0XEBRzBN0-blP9SJkD66o3MCV3aegBAkGw-JZc1S6EVHgDBxZPqmImpWJzFoCR08zAc7aeY4z8NIlawRuyygCL1Y5WIa52e_-YcV7_HdVlpQUHydl7A=s0-d)
Action : It is defined in the classical physics by time integration Lagrangian L = (T - V) of a system.
where T is the kinetic-energy and V is potential energy of the system.
Most commonly, the term is used for a functional S which takes a function of time and (for fields) space as input and returns a scalar.
I think the wikipedia is really a good document to have an initial understanding of Classical mechanics and variation calculus.
Key factors of the Quantum mechanics :-
1) Wave-particle duality :- According to De Broglie hypothesis Every wave is a particle and vice-verse.
where h is Planck's constant, E and p are Energy and momentum respectively. More λ is the wavelength and f is the frequency.
2) Light is an accumulation of particle named photon :- Light is a wave and particle according to the De-Broglie hypothesis, the particles of light is called photon.
The nature can be described as the particle interaction as well as the Wave superposition.
This is a nice video of Quantum Object Nature . :)
3) Wave Mechanics :- The behavior of wave particle is been discussed in the wave mechanics.
Schrödinger Equations paved the root of this mechanics.
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