Quantum Mechanic/wave function/junction condition

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Discussion Overview

The discussion revolves around the derivation of equations related to quantum mechanics, specifically focusing on the elimination of constants C and D and the transition between two equations in a mathematical context. Participants are examining the steps involved in this derivation, including potential omissions in the provided equations.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant seeks clarification on how to eliminate constants C and D and requests the intermediate steps between the 4th and 5th equations.
  • Another participant notes that several steps appear to have been skipped, suggesting that one should either trust the author or verify the algebra independently.
  • A third participant offers a perspective on the importance of verifying calculations, comparing the process to eating oatmeal—unpleasant but beneficial in the long run.
  • A fourth participant emphasizes the need for essential context regarding the boundary condition equations and questions the notation used for wave numbers, suggesting a simplification in the subscripts.

Areas of Agreement / Disagreement

Participants express a shared concern regarding the potential omission of steps in the derivation, but no consensus is reached on the specific methods to address these concerns or the correctness of the equations involved.

Contextual Notes

Limitations include the lack of clarity on the assumptions made in the derivation and the dependence on specific definitions of terms such as wave numbers.

GreenTea09
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Junction Condition.jpg

May i know how do i eliminate C and D and how do i obtain the last two equations? Are there skipping of steps in between 4th to 5th equation? What are the intermediate steps that i should take to transit from 4th equation to the 5th equation?
 
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It looks like quite a few steps have been skipped. You either trust the author or check the algebra yourself.
 
Or the best of both worlds: trust, but verify. Doing a messy calculation is like eating oatmeal, not pleasant in the moment but makes things easier later.
 
And for the sake of PF readers: provide essential context so we can see where these boundary condition equations are sitting ! And where the wave number is ##k_i, k_i', k_i''## (hey, can we skip the subscript 1 ?
 

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