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1answer
56 views

Dispersion relation from Hamiltonian

Note: This is obviously for homework so I'm not asking for the answer to be spoon fed, I'm just not understanding the steps I have to take. I have a fairly simple Hamiltonian for a ring tight binding ...
2
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1answer
138 views

Bloch waves at large momenta

I am trying to come to grip with some solid state theory. Bloch waves, energy eigenstates for hamiltonians with lattice periodic potential in $\mathbb R^d$, are frequently written as $$\phi_{n,k}(r)=e^...
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0answers
72 views

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 ...
5
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1answer
293 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). ...
2
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1answer
136 views

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 ...
11
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1answer
307 views

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 ...
4
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3answers
801 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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2answers
240 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 ...