I feel a bit silly asking this, but I've been working through some QM lately and there's one aspect of Schrodinger's equation that's puzzling me. I've typically understood the equation as [itex]i\hbar \frac{d|\psi\rangle}{dt}=\hat H |\psi\rangle[/itex], but I've also seen it written as [itex]i\hbar \frac{\partial |\psi\rangle}{\partial t}=\hat H|\psi\rangle[/itex]. The use of a partial derivative instead of a total derivative is what's got me. In most cases, I know it doesn't matter but I can imagine some where it would. The total derivative indicates that [itex]\psi[/itex] may not explicitly depend on time, but implicitly could through some other variable which is dependent on time. This evolution is generated by the Hamiltonian. In the other case, the partial derivative only concerns explicit time dependence, and hence this form only makes sense to me when there is an explicit [itex]t[/itex] showing up in the equations. Which form is generally correct?(adsbygoogle = window.adsbygoogle || []).push({});

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# Proper form of schrodinger's equation?

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