i'm reading through halzen and martin's chapter 12 on the weak interaction which they calculate the fermi coupling constant form oxygen beta decay using
\Gamma = 1/\tau = G^2E_0^5/30\pi^3
with E_0 = 1.81MeV and \tau log 2 = 71 sec. they get G\approx 10^{-5}/m^2_N. where m_N is the nucleon mass...
Homework Statement
Show that \int^{\infty}_{-\infty} \frac{e^{kx}}{1+e^{x}}dx converges if 0<k<1
Homework Equations
None
The Attempt at a Solution
Well if I can show that the integral is dominated by another that converges then I'm done, but I haven't been able to come up with one...
Homework Statement
I need to find the eigenvalues of the pion triplet under G parity
Homework Equations
G\mid\psi\rangle = CR_2\mid\psi\rangle
The Attempt at a Solution
OK so visually this problem is pretty simple, rotation about the 2 axis takes a pi+ to a pi- and then charge...
Homework Statement
Let P(z)=1+2z+3z^2+...nz^(n-1). By considering (1-z)P(z) show that all the zeros of P(z) are inside the unit disk
Homework Equations
None given..
The Attempt at a Solution
Well (1-z)P(z) = 1+z+z^2+...+nz^n
and to find roots I set it to 0:
1+z+z^2+...+nz^n = 0...