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How the Bloch sphere of a Hahn echo in NMR looks like? 90-t-90-t-echo

I have tried to find in the literature a proper nice and beautiful Bloch sphere to describe the trajectory of a nuclear spin, starting in z-axis, using a pulse sequence of an initial 90º pulse with ...
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229 views

Advanced atomic physics: From Liouville Equations to the Bloch equations

I'm trying to derive the Bloch equations from the Liouville equation. This should be possible according to this paper, where it discusses higher order Bloch equations (second order spherical tensors). ...
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Wannier functions on a ring

Let's say I have a single particle hamiltonian in a periodic potential. For example a 1D lattice such that: $$H = -\frac{\partial_x^2}{2m} + V(x) $$ with $ V(x+a) = V(x)$ where $a$ is the lattice ...
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Crystal momentum and the vector potential

I noticed that the Aharonov–Bohm effect describes a phase factor given by $e^{\frac{i}{\hbar}\int_{\partial\gamma}q A_\mu dx^\mu}$. I also recognize that electrons in a periodic potential gain a phase ...
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2answers
544 views

How does Bloch's theorem generalize to a finite sized crystal?

I would be fine with a one dimensional lattice for the purpose of answering this question. I am trying to figure out what more general theorem (if any) gives Bloch's theorem as the number of unit ...
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206 views

Bloch oscillations - Scattering to other bands

In the free electron approximation, a Bloch state $|k\rangle$ is the linear superposition of free plane wave states $\sum_G C_G(k) |k+G\rangle$, where $G$ are the conjugate lattice. Since the ...