What is the significance of wave function in schrodingers equation

what is the significance of wave function in schrodingers equation

We solve the equation of motion using the Newton's law. We can get energy also.

But the wave function has all this information. You have to find a suitable operator. That operator will give you the corresponding value. Say a momentum. In classical mechanics directly gives that. In quantum mechanics one must know the corresponding operator. That will give the value. Wave function is a black box. You can put in your hand in and tell it to get the energy. You will get that and take your hand out.

First and foremost, the wavefunction describes the quantum state of a particle and how it behaves. More importantly, perhaps, is it describes how the system of the particle will evolve (change) over time. It's similar to weather forecasting; we have a bunch of rules to describe a dynamical system, and from that are able to deduce what will happen in the future -- how the system will evolve and change. The wavefunction does a similar thing. The wavefunction also allows us to calculate what the probabilities will be of a particle being in a certain place (the square of the wavefunction gives you a 'probability density'). This is applicable in areas such as chemistry where you learn the different atomic orbitals of an electron (1s, 2s, 2p ... etc.). These orbitals are areas where an electron has the highest probability of being -- something we know because of wavefunctions.

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