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    • 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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