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## Main Question or Discussion Point

I have the following system of differential equations, for the functions ##A(r)## and ##B(r)##:

##A'-\frac{m}{r}A=(\epsilon+1)B##

and

##-B' -\frac{m+1}{r}B=(\epsilon-1)A##

##m## and ##\epsilon## are constants, with ##\epsilon<1##. The functions ##A## and ##B## are the two components of a spinor.

By solving the first equation for ##B##, and substituting in the other one, we get a second-order differential for ##A##.Its solutions are modified Bessel functions, and due to the boundary conditions that I have, only those of the first kind are admissable solutions. Having solved for ##A##, going back to the first equation, we can find ##B##. Consequently, ##B=\frac{1}{\epsilon+1}...##. However, in a paper I am studying, the solution to this system is given by ##A=(\epsilon-1)(I_{m})## and ##B=I_{m+1}##. I understand the modified Bessel function part, but the prefactors seem odd to me. Even if we start by solving for ##B## instead of ##A## in the beginning, still ##A## ought to be equal to ##\frac{1}{\epsilon-1} *...## as is given by the second equation. Does anyone have any idea how to reach this result?

##A'-\frac{m}{r}A=(\epsilon+1)B##

and

##-B' -\frac{m+1}{r}B=(\epsilon-1)A##

##m## and ##\epsilon## are constants, with ##\epsilon<1##. The functions ##A## and ##B## are the two components of a spinor.

By solving the first equation for ##B##, and substituting in the other one, we get a second-order differential for ##A##.Its solutions are modified Bessel functions, and due to the boundary conditions that I have, only those of the first kind are admissable solutions. Having solved for ##A##, going back to the first equation, we can find ##B##. Consequently, ##B=\frac{1}{\epsilon+1}...##. However, in a paper I am studying, the solution to this system is given by ##A=(\epsilon-1)(I_{m})## and ##B=I_{m+1}##. I understand the modified Bessel function part, but the prefactors seem odd to me. Even if we start by solving for ##B## instead of ##A## in the beginning, still ##A## ought to be equal to ##\frac{1}{\epsilon-1} *...## as is given by the second equation. Does anyone have any idea how to reach this result?