Calculating % Contribution of nth Wavefunction in Potential Well

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SUMMARY

The discussion focuses on calculating the percentage contribution of the nth wavefunction in an infinite potential well to the classical initial wavefunction, represented as psi(x,t=0) = 1/sqrt(L). The specific wavefunction in question is defined for n=(2x2-1), with a notable exclusion of even n values. Participants suggest that the solution may involve Fourier series and emphasize the importance of understanding the coefficient equation related to energy levels in quantum mechanics.

PREREQUISITES
  • Understanding of quantum mechanics principles, specifically wavefunctions.
  • Familiarity with infinite potential wells and their properties.
  • Knowledge of Fourier series and their application in quantum mechanics.
  • Basic grasp of energy levels in quantum systems.
NEXT STEPS
  • Study the derivation and application of Fourier series in quantum mechanics.
  • Research the properties of infinite potential wells and their wavefunctions.
  • Learn about the coefficient equation for wavefunction contributions in quantum systems.
  • Examine the significance of odd and even quantum numbers in wavefunctions.
USEFUL FOR

Students and educators in quantum mechanics, particularly those studying wavefunctions in infinite potential wells, as well as anyone seeking to deepen their understanding of Fourier analysis in physics.

Caldo120
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Homework Statement



What fraction (as a percentage) does the n=(2x2-1)th infinite potential well wavefunction contribute to the 'classical' initial wavefunction psi(x,t=0)=1/sqrt(L) ? (Why are the even n excluded?)

Homework Equations



psi(x,t=0) = 1 / sqrt(L)

The Attempt at a Solution



generally pretty dumbfounded with this, our lecturer hasn't went through a worked example and i can't find any related equations in my notes. Any help on the question would be greatly appreciated. I intend to ask my lecturer about it as well and the lack of related material. I think it may have something to do with Fourier series?

Thanks,

Calum
 
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use the coefficient equation if you know what that is. And what energy level is that exactly
 

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