Wave Function: Physical Basis of 1st Order Derivative

[phoenixnitc]

What is the physical basis for the requirement that the wave function has finite and continuous first order derivative?

 

[tom.stoer]

b/c only then it carries finite momentum and energy in a finite interval

$$\int_{x-\epsilon}^{x+\epsilon}dy\,\psi^\ast\,(i\partial_y)\,\psi$$

$$\int_{x-\epsilon}^{x+\epsilon}dy\,\psi^\ast\,(-\partial^2_y)\,\psi$$

 

[phoenixnitc]

Thank you.That really helped me a lot.

 

[phoenixnitc]

Why don't we feel the rotation of the Earth when we observe it from a helicopter?

 

[phoenixnitc]

Has "D-WAVE Systems" really developed a quantum computer?

 

[phoenixnitc]

Is there any branch of physics that deals with the neural networks in the brain?

 

[lostprophets]

i was thinking about light.
a particle and/or a wave ?
but what about darkness.?
does darkness move at the speed of light?
does light move at the speed of darkness?
does light really bend around corners or is it pulled around by darkness?
in a dark universe, does the universe expand when light appears?
does light "push" darkness away ?

your thoughts

 

[phoenixnitc]

Darkness is nothing but the absence of light.
One can definitely say that speed of darkness is equal to the speed of darkness as when light travels the darkness vanishes away.
Light pushes the darkness and darkness has zero resistance in stopping the light.
I guess that the expansion of universe has nothing to do with the light as it is expanding because of the bodies that are travelling.