Solving the Schrödinger Equation for Quantum Harmonic Oscillators.
<p>The Schrödinger equation can be thought of as the equivalent to the Newton’s second law but in the quantum world. In the Schrödinger equation, the <strong>wave function (Ψ) </strong>is used to describe the quantum particle. The quantum<strong> Hamiltonian (H)</strong> is an operator which corresponds to the kinetic and potential energy of the system. The Hamiltonian operates on the wavefunction giving a set of <strong>energy eigenvalues</strong> which are the possible values of the energy of the system.</p>
<p>Now back to our harmonic oscillator system. How can we describe it quantumly? First, we develop the Hamiltonian operator into the <strong>kinetic</strong> and the <strong>potential</strong> energy parts:</p>
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