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[Phys-L] phase of a classical wavefunction



Suppose you write down the phase for a wave on a string traveling in the +x
direction as (kx-wt). Do you write the phase for a wave traveling in the -x
direction as (kx+wt) or as (-kx-wt), ie. which sign do you reverse: the one
in front of kx or the one in front of wt?

One might say it doesn't matter. But in some contexts, it can. For example,
suppose I describe an incident sinusoidal wave as A sin(kx-wt) and the
reflected wave as A sin(kx+wt) off a free end of the string at x=0. That
reflected wave has the wrong sign: at x=0 the incident wave has positive
sign at t=0+ but the reflected wave has negative sign. If we write the
reflected wave instead as A sin(-kx-wt) then it has the expected positive
sign for an uninverted reflection.

One person suggested to me that it makes sense to change the sign of k
because that's proportional to momentum, whereas it doesn't make sense to
change the sign of w because that's a frequency. For a complex wave, he
suggested we like to keep the sign of the exp(iwt) term alone and only
fiddle with the sign of the exp(ikx) piece.

Do you agree with that suggestion? Is there another way to look at this
situation?

--
Carl E Mungan, Assoc Prof of Physics 410-293-6680 (O) -3729 (F)
Naval Academy Stop 9c, 572C Holloway Rd, Annapolis MD 21402-1363
mailto:mungan@usna.edu http://usna.edu/Users/physics/mungan/