In Griffith's "Introduction to Quantum Mechanics, second edition" he states: For the delta-function potential, when considering the scattered states (with E > 0), we have the general solutions for the time-independent Schrodinger equation: $$\psi(x) = Ae^{ikx} + Be^{-ikx}~~~~\text{for }x<0$$ and $$\psi(x) = Fe^{ikx} + Ge^{-ikx}~~~~\text{for }x>0.$$ In a typical scattering experiment, particles are fired in from one direction-let's say, from the left. In that case the amplitude of the wave coming in from the right will be zero: $$G=0~~~~~(\text{for scattering from the left}).$$(adsbygoogle = window.adsbygoogle || []).push({});

Then A is the amplitude of the incident wave, B is the amplitude of the reflected wave and F is the amplitude of the transmitted wave. Now the probability of finding the particle at a specified location is given by $$|\Psi|^2,$$ so the relative probability that an incident particle will be reflected back is $$R \equiv \frac{|B|^2}{|A|^2}$$ where R is called the reflective coefficient.

Question:

How does the definition of R follow? Where exactly does this probability come from?

Thanks for any assistance.

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# I Why is reflection coefficient defined this way

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