# Tagged Questions

For questions about problems related to physics that involve evaluating integrals. Purely mathematical questions should be asked at math.SE.

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### Showing $\frac{d^3\underline{k}}{2\omega_{k}(2\pi)^3}$ is Lorentz invariant [duplicate]

Show $\frac{d^3\underline{k}}{2\omega_{k}(2\pi)^3}$ is Lorentz invariant. Hint: try to evaluate $\int dk_0\delta(k_0^2 - M^2)\theta(k_0)$ where $M^2 = \underline{k} + m^2$ My attempt is as ...
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### Integration to find general solution of free particle [closed]

I was attempting problems in Griffiths Intro to QM when I came across the following: A free particle has the initial wavefunction: $$\Psi(x, 0) = Ae^{-ax^2} \, .$$ Find $\Psi(x, t)$. I ...
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### How does Galitskii's integral converge?

In V M Galitskii's 1958 paper "$\textit{Energy spectrum of a non-ideal Fermi Gas}$," he builds the following integral as part of a longer expression for the real part of the self-energy (eqn 26'). It ...
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### Do wave functions really belong to $L^2$ space, or do we need to restrict our physical Hilbert space even further?

I am beginning to study quantum mechanics and I got stuck right at the beginning. I am trying to prove that the time derivative of the expected value of momentum of a particle is the (negative) ...
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### Calculate distance with variable acceleration [duplicate]

I know the time and I know the force that acts horizontally on a particle. The problem is that the force is F=k(D-V), where k and D are constants. So at the beginning where the particle has zero ...
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### Cancelling the partial of a coordinate, $\partial q$, with the element of a coordinate, $dq$ in Physics [closed]

I've seen in many books, things like this ( I will be simple ): $$\int \frac{\partial f}{\partial q} dq=\int df$$ where $f$ is a function of $q$ and other coordinates. I just axiomatically assumed ...
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### How to intergate the cross section over the surface of a detector?

My beam moves along the $X$ axis. I know the cross section $\frac{d \sigma}{d \Omega}$. My rectangular detector is perpendicular to the $XY$ plane and its surface is perpendicular to the line ...