The operator $X^{-2}$ does exist and is self-adjoint as it follows from standard spectral theory. Its domain is $$D(X^{-2}) := \left\{\psi \in L^2(\mathbb R, dx) \:\left|\: \int_{\mathbb R} x^{-4} |\psi(x)|^2 dx \right.< +\infty\right\}$$ and thereon
$$(X^{-2}\psi)(x) := x^{-2}\psi(x)\:.$$
The e...
The post I speak of is below.
What does the discovery of a pentaquark signify?
Whilst OP has hardly been perfect in their articulation of the question, it does to me seem to be clear what they're asking. They want to know about what the discovery of the Pentaquark means for physics.
Popular me...
I am following the conventions of http://isites.harvard.edu/fs/docs/icb.topic1146665.files/III-9-RenormalizationGroup.pdf. Consider the QED Lagrangian
$$-\frac{1}{4}Z_3F_{\mu\nu}^2+Z_2\bar{\psi}i\gamma^{\mu}\partial_{\mu}\psi-Z_2Z_mm\bar{\psi}\psi+Z_eZ_2\sqrt{Z_3}e\bar{\psi}\gamma^{\mu}A_{\mu}\p...
I am reading about Euler-Lagrange equations and this particular section is a little unclear. Consider the differential equation
$$\begin{bmatrix}
\dot{x}\\
\dot{y}
\end{bmatrix} = \begin{bmatrix}
-7x^{\frac{6}{7}}y^{\frac{1}{7}}\\
7x^{\frac{1}{7}}y^{\frac{6}{7}}
\end{bmatrix}\quad (x(0),y(0)) = ...
