How Do You Derive the Schrödinger Equation from Classical Expressions?

PhysicalProof · Apr 22, 2010

Homework Statement

Problem text on mirror electron microscopy: an electron incident on a negatively charged cathode at potential difference ΔV from an anode, with potential energy V(z) = (eΔV/L) z, and a request to derive the time-dependent Schrödinger equation via canonical quantisation.

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 · Apr 23, 2010

Anyone have an idea? :(

PhysicalProof · Apr 25, 2010

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

How Do You Derive the Schrödinger Equation from Classical Expressions?

Homework Statement

Homework Equations

The Attempt at a Solution

Discussion

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