# Wavefunction conditions

1. May 27, 2007

### r-dizzel

hey all!
does anyone know the conditions a well behaved wavefunction (phi) must satisfy for all x? and any physical justifications for them?

is it something to do with continuity at boundaries? or to do with the differential of the wavefunction?

cheers for any input

roc

2. May 27, 2007

### cristo

Staff Emeritus
In QM a well behaved function is generally a function that is continous and finite everywhere, and whose first derivative is continous and finite everywhere also.

3. May 27, 2007

### Staff: Mentor

Last edited by a moderator: Apr 22, 2017
4. May 27, 2007

### r-dizzel

cheers for the help gents!

5. May 27, 2007

### r-dizzel

as far as the physical justification for the constraints, are there any?

6. May 27, 2007

### say_physics04

agreed... well defined,,

anything else?

Last edited: May 27, 2007
7. May 27, 2007

### Dr Transport

A wave function blowing up at infinity isn't really a good thing is it????

8. May 27, 2007

### cristo

Staff Emeritus
Erm... I'm not sure I know what you're getting at!

9. May 28, 2007

### StatMechGuy

The modulus squared of the wave function is a probability distribution. Is there any physical reason to say that at the point $$x = 0 + \epsilon$$ there's one probability density, and then at $$x = 0 - \epsilon$$ it's wildly different?

Also, the continuous first derivative rule comes from a similar notion with regards to the momentum. I'll leave it to you to figure that one out.