Does the Phase Factor in Wave Function Matter?

[captain]

does a phase factor (that can be represented by an imaginary exponential) in psi (the wave function) really matter? I am doing a problem and getting an answer that looks like sin[n(pi)x/a] when the answer is actually sin[n(pi)x/a-n(pi)]. I am just wondering at all if it makes any defference in the scheme of things. are both answers correct (because i know the probability will still be the same)?

 

[pam]

If n is an integer, then trigonometry shows that the two sins are the same..

 

[akhmeteli]

If n is an integer, then trigonometry shows that the two sins are the same..

up to a sign, as far as I remember trigonometry.

 

[captain]

up to a sign, as far as I remember trigonometry.

i understand that but are they both the same answer for a probability amplitude that fits the boundary conditions and where n in the form above is an integer?

 

[akhmeteli]

i understand that but are they both the same answer for a probability amplitude that fits the boundary conditions and where n in the form above is an integer?

You see, now you are supplying more details. Now your question sounds less philosophical and more mathematical. Why don't you just formulate the problem in its entirety, and then we might opine whether both answers are equally satisfactory.

 

[pam]

i understand that but are they both the same answer for a probability amplitude that fits the boundary conditions and where n in the form above is an integer?

If $$\psi$$ is a wave function, then $$e^{i\phi}\psi$$ is an equivalent wave function. In you case $$\phi=n\pi$$. -sin kx is equivalent to +sin kx.