[Q] Sign of wavefunction in PIB

In summary: So for ANY point other than the one at which the wavefunction is EXAKT, there is a probability of finding the particle there. But because there is a probability at the node, it means that the particle could be found at ANY point along the half-length between the node and the original position of the particle in the box. In summary, the sign of the wavefunction indicates whether the wavefunction is positive or negative at a particular point in space.
  • #1
Alice Jin
18
0
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.
 
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  • #2
WHAT sign? Clarify.
 
  • #3
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?
 
  • #4
You mean that the wave function attain both postive and negative values?

What is the strange thing about that, what make you want to ask this question?
 
  • #5
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.
 
  • #6
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.
 
  • #7
Then, how can you explain the sudden probability change in a node?
 
  • #8
define "sudden" change, I don't think that is a mathematical term..
 
  • #9
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?
 
  • #10
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...
 

1. What is the "sign" of a wavefunction in a particle in a box (PIB)?

The "sign" of a wavefunction in a PIB refers to the positive or negative amplitude of the wavefunction at a given point in space. It represents the probability of finding the particle in that particular position.

2. How does the "sign" of a wavefunction affect the behavior of a particle in a box?

The "sign" of a wavefunction does not affect the behavior of a particle in a box. It is simply a mathematical representation of the probability of finding the particle at a specific point in space.

3. Can the "sign" of a wavefunction be negative?

Yes, the "sign" of a wavefunction can be negative. This indicates that there is a higher probability of finding the particle in that specific position with a negative amplitude.

4. How is the "sign" of a wavefunction determined in a PIB?

The "sign" of a wavefunction is determined by solving the Schrödinger equation for a particle in a box. The resulting wavefunction will have both positive and negative values, representing the probability of finding the particle at different positions.

5. What is the physical significance of the "sign" of a wavefunction in a PIB?

The physical significance of the "sign" of a wavefunction is that it represents the probability of finding the particle in a specific position in space. This is a fundamental concept in quantum mechanics and helps us understand the behavior of particles at the subatomic level.

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