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    • 1.7: The Green's Function for a Free Particle
      https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Mechanics_III_(Chong)/01%3A_Scattering_Theory/1.07%3A_The_Green's_Function_for_a_Free_Particle
      We have defined the free-particle Green’s function as the operator G^0=(E−H^0)−1 . Its representation in the position basis, ⟨r|G^0|r′⟩ , is called the propagator. As we have just seen, when the Bor...We have defined the free-particle Green’s function as the operator G^0=(E−H^0)−1 . Its representation in the position basis, ⟨r|G^0|r′⟩ , is called the propagator. As we have just seen, when the Born series is written in the position basis, the propagator appears in the integrand and describes how the particle “propagates” between discrete scattering events.
    • 6.1: Time-dependent Schrödinger Equation
      https://phys.libretexts.org/Bookshelves/Nuclear_and_Particle_Physics/Introduction_to_Applied_Nuclear_Physics_(Cappellaro)/06%3A_Time_Evolution_in_Quantum_Mechanics/6.01%3A_Time-dependent_Schrodinger_equation
      \[\begin{array}{c} \left|c_{1}(0) e^{-i \omega_{1} t} \varphi_{1}(x)+c_{2}(0) e^{-i \omega_{2} t} \varphi_{2}(x)\right|^{2} \\ =\left|c_{1}(0)\right|^{2}\left|\varphi_{1}(x)\right|^{2}+\left|c_{2}(0)\...\[\begin{array}{c} \left|c_{1}(0) e^{-i \omega_{1} t} \varphi_{1}(x)+c_{2}(0) e^{-i \omega_{2} t} \varphi_{2}(x)\right|^{2} \\ =\left|c_{1}(0)\right|^{2}\left|\varphi_{1}(x)\right|^{2}+\left|c_{2}(0)\right|^{2}\left|\varphi_{2}(x)\right|^{2}+c_{1}^{*} c_{2} \varphi_{1}^{*} \varphi_{2} e^{-i\left(\omega_{2}-\omega_{1}\right) t}+c_{1} c_{2}^{*} \varphi_{1} \varphi_{2}^{*} e^{i\left(\omega_{2}-\omega_{1}\right) t} \\ =\left|c_{1}\right|^{2}+\left|c_{2}\right|^{2}+2 \operatorname{Re}\left[c_{1}^{*}…

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