Question about wave function and 1 dimensional well

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SUMMARY

The discussion centers on the analysis of a wavefunction for a particle in a one-dimensional potential well. The participant concludes that the correct potential corresponding to the given wavefunction is option C, as the wavefunction indicates that the wavelength decreases with increasing x. This decrease in wavelength implies an increase in kinetic energy, which corresponds to a decrease in potential energy, validating the choice of potential energy profile in option C.

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  • Understanding of quantum mechanics principles, specifically wavefunctions.
  • Familiarity with potential wells in one-dimensional quantum systems.
  • Knowledge of the relationship between wavelength, kinetic energy, and potential energy.
  • Basic proficiency in interpreting mathematical equations related to wavefunctions.
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  • Study the properties of wavefunctions in quantum mechanics.
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Students of quantum mechanics, physics educators, and anyone interested in the behavior of particles in potential wells will benefit from this discussion.

fredrogers3
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Homework Statement


Present is a wavefunction of a particle in a 1-dimensional well. Choose the correct potential that could result in this wave function:

p214h4.b5.gif


Homework Equations


See below

The Attempt at a Solution



I want to make sure I am analyzing this correctly. I think the correct answer here is C. In the wavefunction, it looks as if the wavelength gets shorter as x increases. Thus, doesn't that mean that potential energy decreases, as is seen in C? When wavelength gets shorter, kinetic energy increases at the expense of potential energy.
Is that correct?
 
Last edited:
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Yes, that's correct.
 

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