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elduderino
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I was reading Merzbacher and it is written that it is a fundamental mathematical assumption. I was doubting if it is an assumption at all.
We get the principle of superposition when we solve certain kinds of differential equations (second order, first degree or linear) where we get as solutions linearly independent functions which span the functional basis [tex]\{ \sin x,\cos x \} [/tex] or [tex] \{ e^{ix}, e^{-ix} \} [/tex]. It is by nature of these solutions that the entire basis can be spanned, and by the linear nature of the differential equations that any linear combination of this basis set can be represented as a solution.
Why does Merzbacher still call it a mathematical assumption? Where am I wrong in my understanding.
We get the principle of superposition when we solve certain kinds of differential equations (second order, first degree or linear) where we get as solutions linearly independent functions which span the functional basis [tex]\{ \sin x,\cos x \} [/tex] or [tex] \{ e^{ix}, e^{-ix} \} [/tex]. It is by nature of these solutions that the entire basis can be spanned, and by the linear nature of the differential equations that any linear combination of this basis set can be represented as a solution.
Why does Merzbacher still call it a mathematical assumption? Where am I wrong in my understanding.