Schrödinger Wave Equation is a mathematical expression which describe the energy and position of the electron in space.
The Bohr's model violates the uncertainty principle. So, the correct theory is expected to deal with the probability of finding an electron in a given space.
Schrödinger think over the de-Broglie wave particle duality principle and worked out a mathematical equation using the principle of quantum mechanics.
Schrödinger assumed that nucleus is surrounded by a vibrating electron which are produced by the vibration of a stretched string. He considered if 'x' is the displacement of the electron wave of amplitude 'Ψ' and wave length 'λ' then the value of 'Ψ' in one dimention is given by the sin wave equation.