- #1
smallgirl
- 80
- 0
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.
[/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.