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 [tex]\psi[/tex] is a wave function, then [tex]e^{i\phi}\psi[/tex] is an equivalent wave function. In you case [tex]\phi=n\pi[/tex]. -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?
The phase factor in a wave function is a complex number that represents the overall phase of the wave. It is often denoted by the Greek letter phi (φ) and can be thought of as the "starting point" of the wave.
The phase factor can affect the amplitude and/or the frequency of the wave function. It determines the interference patterns and overall behavior of the wave, such as whether it is constructive or destructive.
Yes, the phase factor can be changed or manipulated through various methods such as applying a phase shift or using a phase plate. This can be useful in controlling the properties of the wave and studying its behavior.
Yes, the phase factor has physical significance as it directly relates to the energy of the wave. It is also important in determining the state of a quantum system and can be measured experimentally.
The phase factor can affect the probability distribution of a wave function by changing the interference patterns and altering the amplitudes of different points in space. This can impact the likelihood of finding a particle at a certain location in a quantum system.