The condition for normalization for a ket vector is $$\langle A \mid A\rangle = 1.$$ However, to test if ket $\mid A \rangle$ is normalized, should I form the inner product with its complex conjugate $\langle A^* \mid$? How do I obtain the $\langle A \mid$ in the equation?

The source of an electromagnetic field is a distribution of electric charge, $\rho$, and a current, with current density $\mathbf{J}$. Considering only Faraday's law and Ampere-Maxwell's law: $$ \nabla\times\mathbf{E}=-\frac{\partial\mathbf{B}}{\partial t}\qquad\text{and}\qquad\nabla\times\mathbf...

Considering a light wave traveling from the vacuum to air, I am trying to find what will happen to its wavelength. At first, using optics, we know that: $$n=\frac{c}{v}$$ where $n$ represents the refractive index. As $n_{vac}=1$: $$n_{air}= \frac{\lambda_{vac}}{\lambda_{air}} \iff \lambda_{ai...

I understand the equation explaining angles of refraction related to wavelengths. But I'm looking for a more intuitive approach/visual explanation? Perhaps related to QM?