Why is the complex conjugate of a TISE solution also a solution?

[gimak]

Homework Statement

Lets say f(x) is a solution to TISE. If it is, why is its complex conjugate f*(x) a solution too?

Homework Equations

TISE = time independent Schrödinger equation

The Attempt at a Solution

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[BvU]

You can convince yourself by showing that $$H\Psi = E\Psi\Rightarrow (H\Psi)^* = (E\Psi)^*$$