The discussion revolves around the significance of phase factors in wave functions, particularly in the context of quantum mechanics. Participants explore whether different representations of wave functions, specifically those differing by a phase factor, yield the same physical predictions, especially regarding probability amplitudes and boundary conditions.
Participants express differing views on the implications of phase factors in wave functions. While some agree that the two forms of the sine function are equivalent under certain conditions, the broader question of their significance in quantum mechanics remains contested.
The discussion does not resolve whether the phase factor has implications beyond mathematical equivalence, leaving open questions about its physical significance in different contexts.
pam said:If n is an integer, then trigonometry shows that the two sins are the same..
akhmeteli said:up to a sign, as far as I remember trigonometry.
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.captain said: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.captain said: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?