So in Griffith's (ed. 2 page 37) there's an equation that says that(adsbygoogle = window.adsbygoogle || []).push({});

**pretend the h's are h-bars...I don't know Latex very well**

ih[itex]\frac{1}{\varphi}[/itex][itex]\frac{d\varphi}{dt}[/itex]=-[itex]\frac{h^{2}}{2m}[/itex][itex]\frac{1}{\psi}[/itex][itex]\frac{d^{2}\psi}{dx^{2}}[/itex]+V

Since in this simplified case V where is a function of x alone he says that each side is equal to a constant but I'm still trying to figure out why.

I can see that the LHS is a function of t alone because he made the wave function separable and the [itex]\varphi[/itex] is a function of t and the [itex]\psi[/itex] is a function of x but I'm not sure why it's important. I see that if we set the equation equal to a constant the rest of the math works out nicely but I can't see what allows us to do this.

If we had say [itex]\frac{dy}{dx}[/itex]=[itex]\frac{dz}{dt}[/itex] and we set the whole thing equal to c, how would I know that y(x) = cx and z(t) = ct (they're the same constant right?) so y(x)/x=z(t)/t ?

Any direction would be great and thank you for your time,

elwin.

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# Stationary States: Differential Equations Issues

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