Identifying potential from wavelength changes in a 1D well

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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:

Four-panel figure: a wavefunction plot of psi against x with wavelength shrinking to the right over a width labelled delta x, above three potential well diagrams A, B and C plotted as U(x) against x, each with the same width delta x.


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?
 
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