How Does Electron Energy Affect Wavelength in a Square Well?

[NeedPhysHelp8]

Square Potential Wells?

Homework Statement

An electron is moving past a square well with energy $$E=3U_{0}$$. What is the ratio of the de Broglie wavelength of the electron in the region x>L to the wavelength for 0<x<L?

Homework Equations

none that I can think of

The Attempt at a Solution

I know that for states of E greater than $$U_{0}$$ the particle is not bound but free to move through all values of x. The free particle wave functions are sinusoidal both inside and outside the well. I think the wavelength should be shorter inside the well than outside because of greater kinetic energy than outside. But how do i prove this?

 

[vela]

How is the particle's energy related to its momentum, and how is its momentum related to its wavelength?

 

[Matterwave]

I suppose, for the de Broglie wavelength, all you need to know is the momentum p. Classically, E (Kinetic) = p^2/2m. Can you go from there?

 

[NeedPhysHelp8]

Hi thanks for the reply,
I understand that E= p^2/2m and then how to find wavelength from there. So that equation is for the kinetic energy outside the potential well for free particle where E=3Uo but what is the energy state inside the well? and why is it greater?

 

[vela]

Energy is conserved. Outside the well, it has K=3U₀ and U=0. Inside the well, U=-U₀, so how much kinetic energy must it have?

 

[NeedPhysHelp8]

oh I think I get it, so inside the well since U=-Uo then K=4Uo so energy is conserved! Thanks a lot Vela appreciate it