Hello! I have two uncertainties (hehe) about two concepts from a QM time-dependent Schrödinger equation video.(adsbygoogle = window.adsbygoogle || []).push({});

The video is

I cannot move on further if I don't fully grasp everything he explains in the video. My two issues are:

1) The general solution for the time-dependent Schrödinger equation starts at 55:20.He uses αi for a set of coefficients of states. What exactly are these? the probability densities? probability amplitudes? the absolute probabilities? He mentions any state vector can be written as a superposition of eigenvectors of the energy, so α should be a probability amplitude, so you can calculate it's squared modulus.

2) At 1:03:04 he comes up with the exponential solution e^-iEjt. Where exactly from does he gets α(0) from?

Appreciating any kind of answer which would help me shed some light on these two things. Cheers!

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# General solution for the time-dependent Schrödinger equation

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