Is the Wave Equation at Infinity Always Zero?

[Niles]

Homework Statement

Hi all.

The wave equation at plus/minus infinity is zero:

$$\left. {\left| {\psi (x,t)} \right| } \right|_{ - \infty }^\infty= 0$$

Does this also mean that:

$$\left. {\left| {\psi (x,t)} \right|^2} \right|_{ - \infty }^\infty=0$$
?

 

[wbrigg]

no.

An interpretation of the square of the wavefunction is the probability of finding it somewhere; i.e.$$\int^{a}_{b}|\Psi(x,t)|^{2}dx$$ is the probability of finding the particle between a and b. you're looking at the probability of finding the particle inbetween +/-$$\infty$$. I.e. anywhere.

 

[Niles]

I'm not talking about the integral, but only the square of the norm of it. So I am only looking at the probability of finding the particle at exactly + and - infinity.

Will this equal zero?

 

[wbrigg]

oh, yeah. 0 squared is zero.