KWhat conditions must a wavefunction satisfy for all values of x?

[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

 

[cristo]

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

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

 

[Doc Al]

Try this for a start: http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/qm.html#c4"

 

[r-dizzel]

cheers for the help gents!

 

[r-dizzel]

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

 

[say_physics04]

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

agreed... well defined,,


anything else?

 

[Dr Transport]

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

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

 

[cristo]

agreed... well defined,,


anything else?

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

 

[StatMechGuy]

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

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.