- #1
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]
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}} ##
[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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