I'm sorry, but the Schrödinger equation cannot be derived. Instead it was postulated by Erwin Schrödinger in 1925 and then later found to be useful in describing quantum mechanical particles.

However, if you are specifically talking about the Schrödinger equation of, say the electron in a hydrogen atom, forming an orbital, that can be derived. You would start off with the Coulomb potential for the nucleus and go on from that.

Is that what you would like me to do?
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