Question

explain about quantum theory in easy way..

Answer 1

Quantum mechanics, substantially, deals with atomic and nuclear phenomena. Nevertheless its development, comes from Classical Mechanics, please keep in mind the commutation relationships between position and momentum, developed using the Hamiltonian or Lagrangian formalism. Now the same relationships hold in Quantum Mechanics, of course those values are modified in order to introduce the

Planck's constant, according to the famous Heisenberg's Uncertainty Principle.
The major differences between Quantum Mechanics and Classical Mechanics are:
1) the physical quantities of interest for us, are now represented by matrices, more precisely, by Hermitian Matrices;
2) the measured values for each of those physical quantities, for example, momentum, and position, are given by the so called eigenvalues of the corresponding matrix which in turn represents the corresponding physical quantity
For example the possible values of the z-projection of the angular momentum of an electron, inside an atom, are given by the eigenvalues of the matrix (operator) which represents that projection of angular momentum, usually denoted with the symbol L_z

3) for each measured value, there is a probability that the value can occur at the same measure process with the same initial condition of that measuring process. Of course the sum of those probabilities, performed over the possible states of our electron, or more generally quantum system, has to be equal to 1.

4) the concept of a state in Quantum Mechanics, is a new concept, and it is not present in Classical or Hamiltonian Mechanics. A state in Quantum Mechanics, indicates a state of a quantum system, with definite value of certain physical quantity. For example, we can speak about a definite state of the spin angular momentum of an electron, which means that the spin angular momentum of that electron has definite eigenvalues, and each eigenvalue has a definite probability associated.

5) a particle, under certain condition, is described now, with a special function, the so called wave function, and such function obeys to the famous Schroedinger Equation, which is a partial differential equation. The meaning of that wave function is the probability to find our particle, into a well defined zone of the euclidean space.