In my research project I arrived at a particular case where the energy spectrum is given by the following transcendental equation(adsbygoogle = window.adsbygoogle || []).push({});

[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?

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# Equivalent expressions

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