Word Count : 319

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To solve the problem numerically, we need to determine the time evolution of the initial state of a two-state quantum system. The system has orthonormal energy eigenkets \(|E_1\rangle\) and \(|E_2\rangle\) with corresponding eigenvalues \(E_1\) and \(E_2\). The initial state of the system is given by: \[ |\psi(0)\rangle = \frac{1}{\sqrt{2}}|E_1\rangle + \frac{1}{\sqrt{2}}|E_2\rangle \] The time evolution of a quantum state in a two-state system is governed by the Schrödinger equation. The time-evolved state \(|\psi(t)\rangle\) can be written as: \[ |\psi(t)\rangle _______ _______ ______ ___ ______ ______ _________ ___.
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