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Not necessarily. A continuous Fourier transform, \frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}e^{-i\omega x}f(x) dx = F(\omega) for example, will give you the Fourier transform of a function over the real line (or in Hilbert space terms, the components of the function in the Fourier basis)...

Hilbert spaces are used so you can treat functions like vectors. If you have a function F(x) defined between, say, a and b, well, kF(x) is also a function; and kF(x) + mG(x) is also a function; and there's a 0 function and an additive inverse and so on. So the set of all functions defined...

This sounds like a pop-science explanation of quantum tunneling. Classically, a charged particle will not be able to 'walk through a wall' (penetrate a barrier of electrical charge) if its kinetic energy is less than the potential energy of the barrier. In quantum mechanics, there's a small...

I see it now. Thanks, folks.

I'm having problems with the equations leading up to eqn 2.45 on page 25. The hamiltonian has a (\nabla\phi)^2 + m^2 \phi^2 term in the \phi(x) commutator and in the \pi(x) commutator it's \phi(-\nabla^2 + m^2) \phi. I'm aware of a vector calculus identity that makes (\nabla\phi)^2 = 1/2...

Because its Compton wavelength is bigger than its Schwarzschild radius.

Now I got it. Never mind, y'all.

Hint: log( A B^z ) = log(A) + log(B^z) = log(A) + z log(B)

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Homework Statement I'm having trouble with e-muon scattering. Tree level, no loops. (This is problem 7.26 in Griffiths Intro to Elem Particles). I get that the amplitude is as stated in the text, but I am having problems coming up with a number when the momenta and spins are added in...