Electron beam with kinetic energy [tex] E_{k} = 10 eV[/tex] strikes a positive potential barrier [tex] V_{0}[/tex] and the kinetic energy after the beam has passed through the barrier is [tex] E_{k} = (10 eV -V_{0})[/tex].(adsbygoogle = window.adsbygoogle || []).push({});

How big potential [tex] V_{0}[/tex] is needed so that 40% of the electron beam is going to be reflected?

What would happen if we now make the potential negative so the electron beam will gain the kinetic energy?

I would say that the energy of the particles is higher than the energy of the potential barrier, thats why we observe transmission and reflection

solving The Schrödinger equation

[tex] \frac{\partial^2}{\partial x^2}\psi(x)+\frac{2m}{\hbar^2}[E-V(x)]\psi(x)=0[/tex]

then the solutions will be

[tex] \psi_{1}=Ae^{ik_{1}x}+Be^{-ik_{1}x}[/tex] in the region x<0 [tex] k_{1}= \sqrt{\frac{2mE}{\hbar^2}}[/tex]

[tex]\psi_{1}=Ce^{ik{2}x}[/tex] in the region x>0 [tex]k_{2}= \sqrt{\frac{2m[E-V_{0}]}{\hbar^2}}[/tex]

the reflection coefficient is [tex] R= (\frac{k_{1}-k_{2}}{k_{1}+k_{2}})^2[/tex]

Can someone help me with the solution?

Is the reflection coefficient going to be 0.4? How to find that value of [tex] V_{0}[/tex]

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# Homework Help: Elektron beam strikes in potential barrier

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