Contour integral and problem of Quantum mechanics (Griffiths)

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SUMMARY

The discussion focuses on solving Griffiths' problem 11.16, which involves deriving a 1-D integral form of the Schrödinger equation using contour integrals. Participants clarify that a contour integral includes only one pole for each contour because a pole contributes solely if it resides within the closed contour. This principle is crucial for understanding the application of complex analysis in quantum mechanics.

PREREQUISITES
  • Understanding of contour integrals in complex analysis
  • Familiarity with the Schrödinger equation
  • Knowledge of poles and residues in complex functions
  • Basic principles of quantum mechanics
NEXT STEPS
  • Study the application of contour integrals in quantum mechanics
  • Learn about poles and residues in complex analysis
  • Explore Griffiths' Quantum Mechanics textbook for additional problems
  • Research the relationship between contour integrals and the Schrödinger equation
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Students of quantum mechanics, physicists working with complex analysis, and anyone tackling Griffiths' problems in quantum theory.

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Homework Statement


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Homework Equations


This is solution of Griffith problem 11.16

The Attempt at a Solution


This is procedure to get a 1-D integral form of Schrödinger equation.
I don't understand why that contour integral include only one pole for each contour?
 

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BREAD said:
I don't understand why that contour integral include only one pole for each contour?
A pole contributes only if it is inside the closed contour. (I could be misunderstanding your question.)
 

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