# Depth of potential well

1. Apr 23, 2015

### Dextrine

1. The problem statement, all variables and given/known data
The odd bound state solution to the potential well problem bears many similarities to the zero angular momentum solution to the 3D spherical potential well. Assume the range of the potential is 2.3 × 10^−13 cm, the binding energy is -2.9 MeV, and the mass of the particle is 940 MeV. Find the depth of the potential in MeV. (The equation to solve is transcendental.)

2. Relevant equations
$$\sqrt{\frac{-E}{E+V0}}=-Cot[\sqrt{\frac{2m(E+V0)}{hbar^2}}a]$$

3. The attempt at a solution

I tried plotting the left and right hand side equations as functions of V0 and found where they intersected. This of course led to infinitely many solutions. The question doesn't ask for the minimum depth of the potential so I'm assuming I am going about this the wrong way.

My minimum depth came out to around 18.5 MeV

2. Apr 24, 2015

### BvU

Hi there,

I followed your calculations, ended up with 18.26 MeV.
This is the lowest value of V0 that gives one odd bound state.
If we interpret the binding energy (ionization energy) as the energy of the lowest odd state, then that way the solution is unique.

3. Apr 24, 2015

### BvU

 strange errors and a double posting !?!? sorry