- #1
Positron137
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In Griffith's Introduction to Quantum Mechanics, on page 56, he says that for scattering states
(E > 0), the general solution for the Dirac delta potential function V(x) = -aδ(x) (once plugged into the Schrodinger Equation), is the following: ψ(x) = Ae^(ikx) + Be^(-ikx), where k = (√2mE)/h. After that, he states that in the general solution for ψ(x) (stated above), both terms do NOT blow up in the section of the well where x < 0. But this doesn't make sense, because earlier, when he was demonstrating bound states (E < 0) , he stated that the second term, Be^(-ikx), blows up at infinity when x < 0. But here, for scattering states, he states that NEITHER term blows up as x < 0, which seems contradictory. Could anyone explain why this is true (why neither term blows up for a scattering state, when x < 0)? Thanks!
(E > 0), the general solution for the Dirac delta potential function V(x) = -aδ(x) (once plugged into the Schrodinger Equation), is the following: ψ(x) = Ae^(ikx) + Be^(-ikx), where k = (√2mE)/h. After that, he states that in the general solution for ψ(x) (stated above), both terms do NOT blow up in the section of the well where x < 0. But this doesn't make sense, because earlier, when he was demonstrating bound states (E < 0) , he stated that the second term, Be^(-ikx), blows up at infinity when x < 0. But here, for scattering states, he states that NEITHER term blows up as x < 0, which seems contradictory. Could anyone explain why this is true (why neither term blows up for a scattering state, when x < 0)? Thanks!
