Finding the minima roots of a potential energy function (using python)

1. Create a new code, define a function to evaluate V(x) and then plot V(x) for a range of x values from 0.01 to 1.00. Use variables to store the numerical values of e ^2 /4pi . ephsalon_naught, A and p, and use units of nm and eV for length and energy, respectively. With the numpy library imported, you can use the function np.exp() to evaluate the exponential term.

2. Calculate the force acting on the particle, F= - dV/dx (by hand), and then create a function to evaluate it. Plot F(x) over the same range as V(x). What value does F(x) take at the minimum of V(x)? Explain why .

3. Differentiate dV/dx to obtain V''(x) and state what you obtain for V'(x) and V''(x).

4. Implement the Newton-Raphson method to find the value of x for which V(x) is minimum, and state it . You should use the plot from step 1 to pick a sensible initial guess.