Talk:Particle in a box
Thanks! A nice, detailed article.
Maybe we should mention that we are using the time-independent Schrödinger equation here, which is different from the one on Schrodinger wave equation. Or maybe that page should be changed.
Also, is it a coincidence that all ψn are real-valued functions? Shouldn't complex numbers show up? --AxelBoldt
Thanks for the compliment on the article. I just added a statement that we are using the time-independent Schroödinger equation. I think it would be useful to add this equation to the Schrodinger wave equation page and explain when its use is appropriate (probably a task for someone more knowledgeable on this subject than myself).
As for the absense of complex numbers, my understanding is that complex numbers, indicate the "phase" of the system and arise in the time-dependent equation. Since the particle in a box is a time-independent problem and corresponds to a standing wave there is no time-dependent portion and hence no complex component to the solution. If anyone more knowledgeable than myself on this subject can confirm or deny this explanation, I would greatly appreciate it.--Matt Stoker
About the doubt above: the wavefunctions for time-independent quantum mechanics problems ARE complex in general, and not necessarily real. The example in this article is simple and compelling because they are real, but in general they can be complex. A simple example of a complex standing wave are the electron states in a hidrogen atom. - Ernesto.