Hello again! This time I have another calculus question for you, coming straight out of my study of the free Schrodinger equation, since I am not that experienced with that kind of derivative.(adsbygoogle = window.adsbygoogle || []).push({});

It all starts with a given wavefunction (which I think is 2-dimensional,correct me if wrong)

[itex]\psi(x,t)=e^{i(px-Et)}/\hbar[/itex] (1)

My book says|: We derive 3.4 according to t and x so we have:

[itex]\frac{\partial \psi}{\partial t}=-\frac{iE}{\hbar} \psi[/itex]

and [itex]\frac{\partial \psi}{\partial x}=\frac{ip}{\hbar}\psi[/itex].

What I don't understand is how this partial deriving works. What I can figure out is that given the (1) equation, you derive the [itex]i(px)/\hbar[/itex] and [itex]i(-Et)/\hbar[/itex] parts differently, one by one not together. Is that it? So you basically remove the e (2.71)(this must be the way to derive from exponential equations, I don't remember clearly though) and derive the power...partially?

Alas, I am confused.. Any understandable link or advice is appreciated!

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# Partial Differentiation in free Schrodinger Equation

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