Quantum mechanics Prove that Schr?dinger's equation is linear by showing that $$ \Psi=a_{1} \Psi_{1}(x, t)+a_{2} \Psi_{2}(x, t) $$ is also a solution of Eq. (5.14) if $\Psi_{1}$ and $\Psi_{2}$ are themselves solutions.
Added by Allison S.
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This means that they satisfy the equation: $$i\hbar\frac{\partial \Psi_{1}}{\partial t} = -\frac{\hbar^2}{2m}\frac{\partial^2 \Psi_{1}}{\partial x^2} + V\Psi_{1}$$ and $$i\hbar\frac{\partial \Psi_{2}}{\partial t} = -\frac{\hbar^2}{2m}\frac{\partial^2 Show more…
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