Re-Write Transcendental Function

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They are there for a reason. In summary, the conversation discusses how to rewrite a transcendental equation in the form x = -tan(bx) and the struggle to eliminate certain variables from the equation.
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James_1978
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1. When solving the Schroedinger equation for the finite potential one can obtain the transcendental equation:

[tex] k_1\cot{k_1 R} = -k_2 [/tex]
2. Where
[tex] k_1 = \sqrt{\frac{2m}{\hbar^{2}}(E+V_{o})} [/tex]
[tex] k_2 = \sqrt{\frac{-2mE}{\hbar^{2}}} [/tex]
The problem 4.6 in Krane (into to nuclear physics) ask to write the above equation in the form:

[tex] x = -\tan{bx} [/tex] where [tex] x = \sqrt{\frac{-(V_{o}+E)}{E}} [/tex]

The Attempt at a Solution



I can rewrite the equation in terms of ## k_1 ## and ## k_2## However, this does get on the form asked. I am unsure how to eliminate ##\frac{2m}{\hbar^{2}}##] and get
## \tan{\frac{-(V_{o}+E)}{E}} ##
 
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1. What is a transcendental function?

A transcendental function is a mathematical function that cannot be expressed using a finite combination of algebraic operations, such as addition, subtraction, multiplication, and division, as well as roots and exponentials. Examples of transcendental functions include trigonometric, exponential, and logarithmic functions.

2. Why would a transcendental function need to be re-written?

A transcendental function may need to be re-written for a variety of reasons, such as simplifying the expression, making it easier to solve or graph, or converting it into a different form for a specific application or problem.

3. How is a transcendental function re-written?

There are various methods for re-writing a transcendental function, depending on the specific function and the desired outcome. Some common techniques include using trigonometric identities, applying logarithmic properties, and using calculus methods such as integration or differentiation.

4. Can a transcendental function be re-written in more than one way?

Yes, a transcendental function can often be re-written in multiple ways. This is because there are often different approaches or techniques that can be used to simplify or transform the function. The most appropriate re-writing method may depend on the specific function and the intended use.

5. What are some common examples of re-written transcendental functions?

Some common examples of re-written transcendental functions include converting trigonometric functions into their equivalent exponential forms, using logarithmic properties to simplify expressions, and transforming complex expressions into simpler forms using calculus methods.

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