image from principles of quantum mechanics why does the off diognal elements of the matrix mediate with the coupling differential equation?

  • $\begingroup$ Well, seems someone mixed up their plurals in that para... $\endgroup$ – user207455 May 18 '19 at 7:10
  • $\begingroup$ Hi and welcome to physics.SE! Please do not post images of texts you want to quote, but type it out instead so it can be indexed by search engines. For formulae, use MathJax instead. $\endgroup$ – ACuriousMind May 18 '19 at 13:27
  • $\begingroup$ ok...it was such a long text thats why i was sorta lazy.. $\endgroup$ – kay May 18 '19 at 16:16

The off-diagonal elements cause the second derivative of $x_1$ to depend on $x_2$ and vice versa. That’s what it means to have coupled differential equations.

If the off-diagonal elements are zero, then you have two uncoupled equations: one for $x_1$ and one for $x_2$.

Uncoupled equations are easier to solve because you can solve each one separately from the other.

  • $\begingroup$ thanks that helped..but solving without diagonlistion shouldnt be wrong,right? $\endgroup$ – kay May 18 '19 at 16:14
  • $\begingroup$ If you can solve them without decoupling them by diagonalizing the matrix, it’s fine to do it that way. (However, if you are in school your teacher may want you to do it in a particular way.) $\endgroup$ – G. Smith May 18 '19 at 16:19

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