Explaining Schrodinger's Equation: Why Is It Linear?

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SUMMARY

Schrödinger's Equation must be linear to ensure that linear combinations of solutions remain valid solutions, adhering to the superposition principle in quantum mechanics. Quantum states are represented as state vectors, or wave functions in position space, which are inherently linear combinations of vectors with complex number components. While there exists a non-linear Schrödinger's equation, the standard formulation is linear, which is crucial for maintaining the consistency of quantum state representation.

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UrbanXrisis
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I was wondering if someone could explain to me why is Schrödinger's Equation has to be linear?
 
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It has to be linear so that also linear combinations of solutions are also solutions of the Schrödinger equation. Quantum states as represented by state vectors ( wave functions in position space) are superposed states, i.e. linear combinations of vectors with complex numbers as their components.

So the superposition principle needs it to be linear.
 
UrbanXrisis said:
I was wondering if someone could explain to me why is Schrödinger's Equation has to be linear?

I can't say anything intelligent about it because I've never studied it, but there IS a non-linear Schrödinger's equation. You could probably Google it.

-Dan
 

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