We can find the energy levels of the particle in the finite square-well potential using the formula for energy of infinite square well.
The formula is given by,
[tex]E_n = n^2 \frac{h^2}{8mL^2}[/tex]
Where
Number of levels (n) = 3
Planck constant (h) [tex]= 6.626*10^{-34}J.s[/tex]
Mass of the particle is (m) [tex]= 1.88GeV/c^2[/tex]
The mass of the particle can be converted to [tex]J/c^2[/tex],
[tex]m=1.88GeV/c^2(\frac{10^9eV}{1GeV})(\frac{1.6*10^{-19}}{1eV})[/tex]
[tex]m=3.008*10^{-10}J/c^2[/tex]
With all the values we can solve in the first equation, so
[tex]E_3 = (3)^2 \frac{h^2}{8mL^2}[/tex]
[tex]E_3 = 9 \frac{h^2c^2}{8mc^2L^2}[/tex]
[tex]E_3= \frac{9(6.626*10^{-34})^2(3*10^8)^2}{8(3.008*10^{-10}/c^2)}[/tex](c^2)(3*10^{-15})}
[tex]E_3 = 1.642*10^{-11}J[/tex]
We can also convert to eV,
[tex]E_3=1.642*10^{-11}J(\frac{1MeV}{1.6*10^{-13}J})[/tex]
[tex]E_3 = 102.62MeV[/tex]
Therefore, the depth of the well needed to contain three energy levels is 102.62MeV
