Why does infinite potential well give rise to standing wave?

[baouba]

For a particle in a box that is described with a wave function, why can there only be a standing wave when there is an infinite potential well? From my understanding, the infinite potential well makes it impossible for the particle to tunnel through the barrier and so the wave function cannot permeate the walls and there is a zero probability of finding the particle on the other side. Is this why there is a standing wave bounded by the walls?

Since we could never have an infinite potential well (That I know of?) does this mean that this is just a generalization and that this is always a probability of finding the particle outside the box?

Can someone let me know if I'm on the right track?

Thanks

 

[Einj]

Yes you are. Since the wave function must exactly vanish on the edges of the well this is, by definition, a standing wave since the total length will always be a multple of $\lambda/2$. Moreover, yes, this is a generalization. The probability of tunneling outside the well will always be finite, even if extremely small in many cases.

 

[jtbell]

The proper word is "idealization", not "generalization."