Radial function in Spherical potential well

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SUMMARY

The discussion focuses on solving the transcendental equation - tan(ka) = k/lambda for a spherical potential well defined by V=0 for 0a. The wavenumber k represents the wave inside the well, while lambda represents the wavenumber outside the well. The solution involves plotting the functions tan(ka) and k/lambda on a graph to find their intersection points, which indicate the conditions for bound states with l=0. The specific equation k/lambda=k^2/2pi is also mentioned for plotting purposes.

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Homework Statement



A Spherical potential which is
0 for 0<r<a
Vo for r>a

Find the condition for bound states, for the radial function with l=0
Plot the result.

The Attempt at a Solution



I have gotten the equation

- tan(ka)=k/lambda
where k is the wavenumber for the wave inside the well and lambda is the wavenumber for the wave outside the wave.
I know these kind of equation have to be solved graphically or numerically. I have a similar equation solved graphically in my textbook but I don't understand it. Can anyone please help me and give me a hint to how to solve this transcendental equation?
 
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You just have to plot the two equations tan(ka) and k/lambda in a single graph. The intersection point between the function tan(ka) and the straight line k/lambda is the answer you need.
 
Except it's not a straight line, because lambda depends on k.
 
I see. Thanks, Avodyne.

Then you have to plot of the graph of tan(ka) and k/lambda=k^2/2pi.
 
I see. Thanks
 
Last edited:

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