Question

what is shrodinger equation

Answer 1

a differential equation which forms the basis of the quantum-mechanical description of matter in terms of the wave-like properties of particles in a field. Its solution is related to the probability density of a particle in space and time.

Answer 2

Yes, the square of the wave function solution [psi] to the equation gives probability density.

Answer 3

For the full Schrodinger equation for the wave function, you would need to see an advanced physics text, which would include its applications to simple situations, such a particle confined between two walls.