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Radial function in Spherical potential well

  • Thread starter Swatch
  • Start date
89
0
1. 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.


3. 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 similiar equation solved graphically in my textbook but I dont understand it. Can anyone please help me and give me a hint to how to solve this transcendental equation?
 

cks

165
0
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.
 

Avodyne

Science Advisor
1,396
85
Except it's not a straight line, because lambda depends on k.
 

cks

165
0
I see. Thanks, Avodyne.

Then you have to plot of the graph of tan(ka) and k/lambda=k^2/2pi.
 
89
0
I see. Thanks
 
Last edited:

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