Plane monochromatic wave is not physically realizable?

[pjbeierle]

I am currently reading Cohen-Tannoudji's Quantum Mechanics. In the book on page 23 there is a comment that states;

"A plane wave of type Ae^i(kx-wt) , whose modulus is constant throughout all space [cf. |ψ|^2=|A|^2], is not square integrable. Therefore, rigorously,it cannot represent a physical state of the particle (in the same way as, in optics, a plane monochromatic wave is not physically realizable). On the other hand, a superposition of plane waves can be square integrable."​

My understanding of what the author is trying to get across is that a wave such as
A*cos(kx-wt) where A=1 integrating from -∞ to ∞ is not finite, fine. but I DON'T understand the optics comment that "a plane monochromatic wave is not physically realizable". I have not taken very much optics or electromagnetic theory, so I have not come across this phenomena. Can someone please explain this to me, or foward me to some reference that will describe trying to physically realize a monochromatic plane wave? thanks

 

[jtbell]

A perfectly pure monochromatic plane wave must extend to infinity in all directions. How does one physically realize such a wave?

If it does not extend to infinity in all directions, then it can be represented (via Fourier analysis) as a superposition of waves with different frequencies, and is therefore not monochromatic.

 

[Ken G]

I'm not sure what importance the distinction really has. Is any square integrable wave function physically realizable? I'm pretty sure that no one here can name a wave function that is physically realizable, so just what that term is actually intended to imply is not so clear.