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Usually, [itex]H[/itex] is an operator, and [itex]E[/itex] is a real number, its eigenvalue. For example, for a free particle,

[itex]H = -\frac{\hbar^2}{2m} \frac{\partial^2}{\partial x^2}[/itex]

When applied to [itex]\psi(x) = e^{ikx}[/itex] you get:

[itex]H \psi = \frac{\hbar^2 k^2}{2m} \psi[/itex]

So for this particular [itex]\psi[/itex], [itex]E = \frac{\hbar^2 k^2}{2m}[/itex], which is a real number.

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