How Do You Derive the Schrödinger Equation from Classical Expressions?

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SUMMARY

The discussion centers on deriving the Schrödinger Equation from classical expressions, specifically focusing on substituting the potential energy function V(z) into the quantum mechanical framework. The participant expresses confusion regarding the conversion of classical potential energy into quantum mechanical terms using operators. The key takeaway is the necessity of understanding the relationship between classical mechanics and quantum mechanics to effectively perform this derivation.

PREREQUISITES
  • Understanding of classical mechanics, particularly potential energy functions.
  • Familiarity with quantum mechanics concepts, specifically the Schrödinger Equation.
  • Knowledge of quantum operators and their application in quantum mechanics.
  • Basic mathematical skills for manipulating equations and expressions.
NEXT STEPS
  • Study the derivation of the Schrödinger Equation from classical mechanics.
  • Learn about quantum operators and their role in quantum mechanics.
  • Explore potential energy functions in quantum systems.
  • Review examples of converting classical expressions to quantum mechanical terms.
USEFUL FOR

Students and researchers in physics, particularly those studying quantum mechanics and its foundational principles, will benefit from this discussion.

PhysicalProof
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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?
 

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