Hi, I am self-studying quantum mechanics and while reading through the derivatio

Question

Hi, I am self-studying quantum mechanics and while reading through the derivation of schroedinger equation I have encountered the necessity of the imaginary unit "i" but I haven't understood exactly the explanation that was given.

The textbook said that the equation contains an i because it relates a first derivative of time with a second derivative of space. Why is it that the only way mathematics can relate a first time derivative to a second derivative of space has to involve the imaginary unit "i"?

if anyone could give me some insight into this it would be very much appreciated!

I'm posting the question in the mathematics section because I'd really like a mathematical point of view on this!

Explanation / Answer

i is known as imaginary unit in complex number system.so,for taking second derivative of space we have to involve i .

Also, If we go geometrically then i is the point on imaginary axis.

And with i 2 = -1.

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