Solving Potential Homework: 6 Eqns, 6 Unknwns & 7 Eqns, 7 Unknwns

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SUMMARY

The discussion addresses solving equations related to quantum mechanics, specifically focusing on the reflection (R) and transmission (T) coefficients for potential barriers. The user encounters a discrepancy where R + T does not equal 1 for the case when E < V0, despite having six equations and six unknowns. The conversation also highlights the complexity of the scenario when E > V0, which involves seven unknowns and six equations. The user suggests converting wavefunctions from exponential to sine/cosine forms to simplify the problem by reducing the number of unknowns.

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  • Understanding of quantum mechanics principles, particularly potential barriers.
  • Familiarity with reflection and transmission coefficients (R and T).
  • Knowledge of solving systems of equations in physics.
  • Experience with wavefunction representations in quantum mechanics.
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  • Research the continuity conditions for wavefunctions at potential boundaries.
  • Study the mathematical derivation of reflection and transmission coefficients in quantum mechanics.
  • Learn about the implications of using sine and cosine functions in wavefunction analysis.
  • Explore advanced techniques for solving systems of equations with more unknowns than equations.
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Students and professionals in physics, particularly those studying quantum mechanics, as well as educators looking for insights into solving complex potential problems involving wavefunctions.

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Homework Statement




I have a question concerning this potential. For E < V0, I have the R and T coefficients, but there sum doesn't equal one, but you have six equations and six unknowns, so its easy to solve I guess.. I have gotten the same answers doing it different ways but can't seem to get R+T=1.

However, it is a lot easier case then solving the case for when E > V0 I have seven unknowns and six equations.

All these equations I have gotten from the continuity requirements. Could I be missing something else?


Could I at least change the interior wavefuntions into sine/cosine since the exponent forms since it's reduces unknowns when matching at zero?

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