- #1

pellman

- 684

- 5

On the Wikipedia page for http://en.wikipedia.org/wiki/Heisenberg_picture#Mathematical_details" we find this relation

[tex]\frac{d}{dt}A(t)=\frac{i}{\hbar}[H,A(t)]+\left(\frac{\partial A}{\partial t}\right)[/tex]

I don't understand what the distinction between

[tex]\frac{d}{dt}A(t)[/tex] and [tex]\left(\frac{\partial A}{\partial t}\right)[/tex]

is supposed to be. That is, what is the difference between the

For regular old c-number functions, the difference between total and partial derivatives is something like

[tex]\frac{df}{dt}=\frac{\partial f}{\partial u}\frac{du}{dt}+\frac{\partial f}{\partial t}[/tex].

where f = f(u,t). If f doesn't depend on other variables, then [tex]\frac{df}{dt}=\frac{\partial f}{\partial t}[/tex].

[tex]\frac{d}{dt}A(t)=\frac{i}{\hbar}[H,A(t)]+\left(\frac{\partial A}{\partial t}\right)[/tex]

I don't understand what the distinction between

[tex]\frac{d}{dt}A(t)[/tex] and [tex]\left(\frac{\partial A}{\partial t}\right)[/tex]

is supposed to be. That is, what is the difference between the

*meaning*of these two expressions?For regular old c-number functions, the difference between total and partial derivatives is something like

[tex]\frac{df}{dt}=\frac{\partial f}{\partial u}\frac{du}{dt}+\frac{\partial f}{\partial t}[/tex].

where f = f(u,t). If f doesn't depend on other variables, then [tex]\frac{df}{dt}=\frac{\partial f}{\partial t}[/tex].

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