# Telling whether a wave function might have physical graph

1. Mar 10, 2013

### Von Neumann

Problem:

Which of the wave functions shown might conceivably have physical significance?

Solution:

I have attached a drawing of the two wave functions. According to my book, the one on the right could have physical significance, while the one on the left does not. Can anyone explain why not? They are both single valued, differentiable functions, so I don't see why the left one is apparently disqualified. Thanks for any help.

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• ###### wavefunction.jpg
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Last edited: Mar 10, 2013
2. Mar 10, 2013

### SammyS

Staff Emeritus

I assume the graph on the left continues upward toward ∞ without a bound.

3. Mar 10, 2013

### Von Neumann

Hmmm, that never occurred to me. How would that take away from its physical significance?

4. Mar 10, 2013

### Von Neumann

Well, since the wave function is proportional to finding the object at a specific place at a specific time, and unbounded wave function doesn't make sense. Right?

5. Mar 10, 2013

### SammyS

Staff Emeritus
Yes.

Why doesn't it make sense?

6. Mar 10, 2013

### Von Neumann

It doesn't make sense logically because, according to the unbounded function, the object described by the wave function is located at an infinite number of places at the same time.

7. Mar 10, 2013

### SammyS

Staff Emeritus
In order for the square of the wave function to represent a probability distribution, what has to be true of the integral of the square of the wave function ?

8. Mar 10, 2013

### Von Neumann

The integral of the square of the wave function must be normalized, correct? Are you hinting that it is impossible to normalize the diverging function?

9. Mar 10, 2013

### SammyS

Staff Emeritus
It is impossible if the integral diverges.