[Q] Sign of wavefunction in PIB

[Alice Jin]

Dear all,

I have a question about the sign of Schrodinger equation in particle in a box.
What's the meaning of the sign (like -, +) of wavefunction in particle in a box?
Can anybody explain that?
Thank you.

[malawi_glenn]

WHAT sign? Clarify.

[Alice Jin]

If you draw the graph of wavefunction of PIB at any state n, the shape oscillates with - and + signs. What's the significance of it?

[malawi_glenn]

You mean that the wave function attain both postive and negative values?

What is the strange thing about that, what make you wanna ask this question?

[Alice Jin]

Why do you ask me like that?
I'm just curious about what the + and - sign of wavefunction stand for.
I know if there is a change of sign, at that point there is a node.
But basically I want to know the meaning of the sign.

[malawi_glenn]

Because sometimes one has thought a bit on why one asks the question, that one has an idea and so on.

There is no meaning about the sign of the wavefunction. The wavefunction is interprented as to the be probability density amplitude, and amplidtudes can attain both positive, negative and Complex values. So there is nothing strange that wave function have some negative and some positive values.

[Alice Jin]

Then, how can you explain the sudden probability change in a node?

[malawi_glenn]

define "sudden" change, I dont think that is a mathematical term..

[Alice Jin]

Ok for the state n=2 in PIB, in the middle of length(x=half lenth) there is a node which means no probability at the point. How do you explain no probability at the point?

[malawi_glenn]

That the particle can't be found there of course. Why is that strange? Forget about classical pictures of particles and motion.

However, the wave function is only EXAKT 0 for ONE point. Now recall from calculus the "length" of a point....