Griffiths QM Problem 4.9 (3rd ed.) Solving the FINITE Spherical Well for l=0

In this video I will solve problem 4.9 as it appears in the 3rd edition of griffiths introduction to quantum mechanics. The problem states:
a particle of mass m is placed in a finite spherical well.

find the ground state by solving the radial equation with l=0. Show that there is no bound state at all if ...

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My name is Nick Heumann, I am a recently graduated physicist. I love to teach physics, so I decided to give YouTube a try. English is not my first language, but I hope that you can understand me well enough regardless.
▬ Contents of this video ▬▬▬▬▬▬▬▬▬▬
00:00 Introducing the problem
01:00 Finding the wavefunction in the inner region (V=0)
08:03 Finding the wavefunction in the outer region (V=V0)
11:37 Applying boundary conditions
13:00 Finding the transcendental equation
17:10 Graphing the equations
22:00 Finding the minimum value for V0 and a

[lowerlowerhk]

This video is really useful. I am reading Townsend and the way he skips the steps on this problem really has me scratching my head.

[anthonypoole]

Thank you for the help the solutions for this book are lifesavers

[MikhailTal-okgk]

I think that in this video there is a mistake because what must satisfy the boundary conditions is the radial function R(r) = u(r) / r. Therefore, the differentiation must be conducted on the R(r) function so you do not have a vanishing term with 1/r, and then you apply r = a. Am I correct?

[MikhailTal-okgk]

I think that in this video there is a mistake because what must satisfy the boundary conditions is the radial function R(r) = u(r) / r. Therefore, the differentiation must be conducted on the R(r) function so you do not have a vanishing term with 1/r, and then you apply r = a. Am I correct?