Please show all intermediate steps for understanding. Thank you. If necessary, p

Question

Please show all intermediate steps for understanding. Thank you. If necessary, provide program or code

evaluate the probability to find an oscillator in the ground state beyond the classical turning points ± x0

This problem cannot be solved in closed, analytic form. Develop an approximate, numerical method using a graph, calculator, or computer

Assume an electron bound to an atomic-sized region ( x0 = 0.1 nm ) with an effective force constant of 1.0 eV/nm2

(To be marked correct, you must be within 25% of the correct answer.)

Explanation / Answer

The wave function for the ground state is Ae^(-a*x^2). So the square of the wave function is A^2*e^(-2*a*x^2), which I will integrate as x ranges from .1 to infinity.
I found A^2 to be 1.0735 nm^-1 and a = 1.8102 nm^-2.
Subsituting these values and integrating yields .394 (probability of finding the oscillator beyond A0).

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