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Quantum Wells: WKB approximation

  1. Mar 26, 2014 #1
    1. Consider a quantum well described by the potential [tex]v(x)=kx^{2}
    [/tex] for [tex]\left|x\right|<a
    [/tex] and [tex]v(x)=ka^{2}[/tex] for [tex]\left|x\right|>a[/tex]. Given
    [tex]a^{2}\sqrt{km}/\hbar
    =2[/tex], show that the well has 3 bound states and calculate the ratios between the energies and [tex]ka^{2}[/tex].
    You may use the standard integral [tex]\intop(1-y^{2})^{1/2}dy=\frac{\pi}{2}
    [/tex]





    I am not sure how to begin the question, really stuck.... Would love some help to get me started.
     
  2. jcsd
  3. Mar 26, 2014 #2
    Have you studied the solution for a harmonic oscillator yet?
     
  4. Mar 26, 2014 #3
    No but I know I'm not meant to do it like that....
     
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