D/dt of <y1|y2> =0 quantum physics

[Chronos000]

Homework Statement

I have to confirm that d/dt $$\int$$ Y₁* Y₂ = 0


So far I have used the product rule to get two expressions.

Then I have used the TDSE to replace dY/dt and dY*/dt. I end up with the line:

(i/$$\hbar$$) [ $$\int$$ H* Y₁* Y₂ - $$\int$$ Y₁* H Y₂ ]

from here I'm not sure where to go. I thought about using the commuator relation but I don't think i can since the operator is at the start of the expression in expression 1.

 

[ideasrule]

What's Y1 and Y2?

 

[Chronos000]

they are just wavefunctions which depend on x and t