- #1
intervoxel
- 195
- 1
In my research project I arrived at a particular case where the energy spectrum is given by the following transcendental equation
[itex]
\sqrt{-\frac{E}{E+V_D}}=\tan\frac{a\sqrt{\frac{2m}{\hbar^2}(E+V_D)}}{2}
[/itex]
In the literature I found the equivalent expression below
[itex]
\cot a\sqrt{-\frac{2m}{\hbar^2}E}=\frac{2E+V_D}{2\sqrt{-E(E+V_D)}}
[/itex]
From the first expression I should get to the second one in order to show the consistency of the theory. But, no matter I have tried, I couldn't find out a solution for this problem.
Can anyone help me, please?
[itex]
\sqrt{-\frac{E}{E+V_D}}=\tan\frac{a\sqrt{\frac{2m}{\hbar^2}(E+V_D)}}{2}
[/itex]
In the literature I found the equivalent expression below
[itex]
\cot a\sqrt{-\frac{2m}{\hbar^2}E}=\frac{2E+V_D}{2\sqrt{-E(E+V_D)}}
[/itex]
From the first expression I should get to the second one in order to show the consistency of the theory. But, no matter I have tried, I couldn't find out a solution for this problem.
Can anyone help me, please?