You studied in the modern physics course (PHYS 212) the solution of one-dimensio

Question

You studied in the modern physics course (PHYS 212) the solution of one-dimensional Schrodinger equation with a finite potential V(x)={V_o o for 0 x a otherwise The analytical solution gives transcendental equations for the even states is alpha tan (alphaalpha)=beta and for the odd states is alpha cot (alphaalpha) =-beta where alpha = squareroot2mE/h^2 and beta = squareroot2m (V_0 - E)h^2 Write a program using python to find the lowest even and the lowest odd solutions to the square well problem using the Newton-Raphson method. You can also use the bisection method. You may plot the above function to get estimates for the initial guess and the interval. Use a = 3 A, m = 1 m_e, V_0 = 10 eV. Plot the wavefunctions associated with these eigenvalues.

Explanation / Answer

def derivative(f, x, h): deriv = (1.0/(2*h))*(f(x+h)-f(x-h)) return deriv def solve(f, x0, h): xn = x0 prev = 0 while ( approx - prev > h): xn = xn - (f(xn))/derivative(f, xn, h) return xn

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