Re-Write Transcendental Function

[James_1978]

Homework Statement

-k_{2} = k_{1}cot(k_{1}R) and rewrite to x = - tan(bx)

Homework Equations

k_{1} = \sqrt{2m(E + V_{o})/ \hbar^{2}} k_{2} = \sqrt{-2mE/ \hbar^{2}} x = \sqrt{-(V_{o} + E)/E}

The Attempt at a Solution

I am unclear how to simplify this equation.[/B]

 

[Ray Vickson]

Homework Statement

-k_{2} = k_{1}cot(k_{1}R) and rewrite to x = - tan(bx)

Homework Equations

k_{1} = \sqrt{2m(E + V_{o})/ \hbar^{2}} k_{2} = \sqrt{-2mE/ \hbar^{2}} x = \sqrt{-(V_{o} + E)/E}

The Attempt at a Solution

I am unclear how to simplify this equation.[/B]

From your equation $-k_2 = k_1 \cot(k_1R)$, what would you get for $\tan(k_1R)$?

BTW: do not write $cot(\cdot)$ and $tan(\cdot)$; these look ugly and can often be hard to read; instead, write $\cot(\cdot)$ and $\tan(\cdot)$. Ditto for $\sin$, $\cos$, $\ln$, $\log$, $\lim$, $\max$, $\min$, $\exp$, etc. You do that by typing "\cot" instead of "cot", etc.

Also, for one-letter subscripts (or superscripts) it is perfectly OK to skip the curly braces, so it works perfectly well to type "k_1" instead of "k_{1}", etc. But, you need braces for sub (super) scripts of more than one character, such as $x_{12}$.

 

[Mark44]

The OP has started a new thread with the same problem. Since the newer thread is closer to the posting requirements, I am closing this thread. Link to new thread: https://www.physicsforums.com/threads/re-write-transcendental-function.936343/#post-5916796