I'm trying to integrate the Schrodinger equation ##i\hbar \frac{d}{dt} |\psi(t)\rangle = H |\psi(t)\rangle## with the initial condition ##|\psi(t_{0})\rangle=|\psi_{0}\rangle##(adsbygoogle = window.adsbygoogle || []).push({});

to show that ##|\psi(t)\rangle = \exp(\frac{t-t_{0}}{i\hbar}H)|\psi_{0}\rangle##.

I know how to plug in the solution into the Schrodinger equation and differentiate the LHS using the Taylor expansion of the exponential of the Hamiltonian operator in order to show that the two sides of the Schrodinger equation are equal.

However, what I'm looking for is an analog/generalisation of the separation of variables technique (used to integrate ordinary first-order differential equations) that works for operators. Can you help me out with it?

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# A Integration of Schrodinger equation

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