How Do You Derive the Schrödinger Equation from Classical Expressions?

AI Thread Summary
The discussion revolves around deriving the Schrödinger Equation from classical expressions, specifically focusing on the potential energy function V(z). The participant expresses confusion about the process and seeks clarification on whether substituting V(z) directly is the correct approach. There is a suggestion that converting the classical expression of V into quantum mechanical terms using operators may be necessary. The need for guidance on the transition from classical to quantum mechanics is emphasized. Overall, the thread highlights the challenges of understanding this fundamental concept in quantum physics.
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Homework Statement



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Homework Equations



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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!
 
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Anyone have an idea? :(
 
I'm thinking that I have to somehow convert that classical expression of V into quantum mechanical terms with operators. Does that sound right?
 
Thread 'Help with Time-Independent Perturbation Theory "Good" States Proof'

Thread 'Help with Time-Independent Perturbation Theory "Good" States Proof'

(Disclaimer: this is not a HW question. I am self-studying, and this felt like the type of question I've seen in this forum. If there is somewhere better for me to share this doubt, please let me know and I'll transfer it right away.) I am currently reviewing Chapter 7 of Introduction to QM by Griffiths. I have been stuck for an hour or so trying to understand the last paragraph of this proof (pls check the attached file). It claims that we can express Ψ_{γ}(0) as a linear combination of...
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