Free electron model Definition and 18 Threads

Fermi energy is given by $$\epsilon_F = \frac{\hbar ^2 k_F ^2}{2m}$$ ##N = \frac{2k_F L}{2\pi} \Rightarrow \frac{k_F L}{\pi}## the factor of two in the numerator comes from the electrons having two spins. $$E=\frac{2L}{2\pi} \int_{0}^{k_F} \frac{\hbar^2 k^2}{2m}\, 2\,dk$$ The two in front of the...

In the following pdf I tried to calculate the density of states of free electrons and phonons. First, I found the free electron DOS in 1D, it turns to be proportional to (energy)^(-1/2) and in 2D it is constant. However, I am not sure I found the DOS for phonons in the second part of the...

This question is more a question I'd ask in a chat rather than formally on paper/forum. If we take the free electron model, the electrons are considered as non interacting. It is essentially a 1 particle problem where the potential is constant through space. The electrons are not perturbed at...

Homework Statement Using free electron model find the number of electron quantum states per unit volume in ##[\varepsilon_F, \varepsilon_F + \Delta \varepsilon]## energy interval of sodium. Fermi energy of sodium is ##\varepsilon_F = 3.22 eV##, and energy band width is ##\Delta...

According to the quantum mechanical free electron model the average energy is E=3EF/5 for the 3D case. Nevertheless I saw in a specialised physics book that for the 1D model the average energy at T=0 is 0 and wanted to know if it is the same for the 3D case.

Homework Statement Nearly free electron model in a 2D lattice. Consider a divalent 2D metal with a square lattice and one atom per primitive lattice cell. The periodic potential has two Fourier components V10 and V11, corresponding to G = (1,0) and (1,1). Both are negative and mod(V10) >...

Hello, I am trying to figure out the width of bands in a 1-dimensional lattice. Here is a short derivation from the book I am reading: if we approximate the free electrons as being in a square well then the energy levels are ## \frac{\pi^2 \hbar^2 n^2}{2mL^2}##. If there are ##N## ions...

Can anybody explain my what is the origin of this forbidden gap? I mean how it was created and what is the physics behind this issue?

Homework Statement (a) Find energies of states at ##(\frac{\pi}{a},0)##. (b) Find secular equation Homework EquationsThe Attempt at a Solution Part(a)[/B] In 1D, the secular equation for energy is: E = \epsilon_0 \pm \left| V(x,y) \right| When represented in complex notation, the potential...

I'm trying to get my head around what this means exactly. I've plotted the graph to help verse me with the functions that I've derived. From the free electron model, the wavefunctions are treated as planewaves of the form \psi_\mathbf{k}(\mathbf{r}) = e^{i\mathbf{k}\cdot\mathbf{r}} Due to...

For a wavefunction at the Brillouin boundary we have: \langle k|H|k\rangle = \epsilon_0 (\vec k) \langle k'|H|k'\rangle = \epsilon_0 (\vec k+\vec G) \langle k'|H|k\rangle = V_G = \frac{1}{L^3} \int e^{i(\vec k - \vec k') \cdot \vec r} V(r) d\vec r \langle k|H|k'\rangle = V_G^* Using...

Hello Physics Forums. Our professor asked us to do a program on constructing the band diagram of BCC and FCC for nearly free electron approximation. what is the best algorithm i can use? i can program a bit, it's just the step-by-step method i am not sure of. thank you

Considering the Nearly Free Electron model of solids, where we assume the valence electrons of some one dimensional(!) solid to move in a weak, periodic (with respect to the solids lattice constant) potensial. We may derive (which I assume you are familiare with, and will not do here) the...

Ok so If I plot ε(k) against k for the nearly free electron model there will be an energy gap. Bragg refelction leads to these energy gaps and standing waves. So does Bragg reflection not ocurr in the free electron model? What materials have the property of the free electron model and what...

Hallo, i would like to know why do we use the term free electron gas instead of Plasma? aren't both the same? thanks, Omri

Hi, In a lot of places it states that one of the great successes of the free electron model is that it gives, more or less, the metallic density of states, I understand that if you do the maths for a fermi gas you end up with a density of states = 3N/2Ef, but to what value do we compare this...

Free Electron Model: Why periodic boundary conditions and what is "L"? Right, hello! The quantum free electron model for electrons in solids (in One dimension) says we need to use periodic boundary conditions such that if Y(x) is the wavefunction, then Y(x) = Y(x+L). Where L seems to be...

Homework Statement This question refers to Kittel's solid-state physics book. I just do not understand the 1D example on pages 164-65. So, I understand everything until the line "The wavefunctions at k = \pm \pi/a are not the traveling waves \exp(i\pi x/a) or \exp(i\pi x/a) of free electrons."...