Question about wave function and 1 dimensional well

In summary, the wave function of a particle in a 1 dimensional well is a mathematical function that describes the probability of finding the particle at a certain position within the well. It is related to the energy of the particle through the Schrödinger equation and is affected by the boundary conditions of the well. The wave function cannot be negative as it represents probability. If the potential of the well is changed, the energy states and shape of the wave function will also change.
  • #1
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?
 
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  • #2
Yes, that's correct.
 

FAQ: Question about wave function and 1 dimensional well

What is the wave function of a particle in a 1 dimensional well?

The wave function of a particle in a 1 dimensional well is a mathematical function that describes the probability of finding the particle at a certain position within the well.

How is the wave function related to the energy of the particle in a 1 dimensional well?

The wave function is related to the energy of the particle through the Schrödinger equation, which describes the time evolution of the wave function and its relationship to the particle's energy.

What is the significance of the boundary conditions in a 1 dimensional well?

The boundary conditions in a 1 dimensional well determine the possible energy states of the particle and the shape of the wave function within the well.

Can the wave function of a particle in a 1 dimensional well be negative?

No, the wave function must be a real-valued function and cannot be negative in a 1 dimensional well. This is because the wave function represents the probability of finding the particle at a certain position, and probabilities cannot be negative.

What happens to the wave function if the potential of the 1 dimensional well is changed?

If the potential of the 1 dimensional well is changed, the energy states and the shape of the wave function will also change. The particle's behavior and probability of being found at different positions within the well will also be affected.

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