How Do You Derive the Schrödinger Equation from Classical Expressions?

[PhysicalProof]

Homework Statement

Homework Equations

This is what I'm trying to obtain, in terms of the elements in the question. Assuming that these 'x' values are 'z'.

The Attempt at a Solution

I'm not really understanding what it is being asked here. Do I just substitute the value of V(z) into obtain the expression? Any advice is appreciated!

 

[PhysicalProof]

Anyone have an idea? :(

 

[PhysicalProof]

I'm thinking that I have to somehow convert that classical expression of V into quantum mechanical terms with operators. Does that sound right?