# What is Free electron model: Definition and 22 Discussions

In solid-state physics, the free electron model is a quantum mechanical model for the behaviour of charge carriers in a metallic solid. It was developed in 1927, principally by Arnold Sommerfeld, who combined the classical Drude model with quantum mechanical Fermi–Dirac statistics and hence it is also known as the Drude–Sommerfeld model.
Given its simplicity, it is surprisingly successful in explaining many experimental phenomena, especially

the Wiedemann–Franz law which relates electrical conductivity and thermal conductivity;
the temperature dependence of the electron heat capacity;
the shape of the electronic density of states;
the range of binding energy values;
electrical conductivities;
the Seebeck coefficient of the thermoelectric effect;
thermal electron emission and field electron emission from bulk metals.The free electron model solved many of the inconsistencies related to the Drude model and gave insight into several other properties of metals. The free electron model considers that metals are composed of a quantum electron gas where ions play almost no role. The model can be very predictive when applied to alkali and noble metals.

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1. ### Phonon density of states and density of states of free electrons

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...
2. ### The Nearly Free Electron Model

This is a multi-part problem. I'm having trouble getting started. Any insights would be greatly appreciated. Prompt: To start off with, I think I'm finding the notation confusing. Specifically I'm not sure what U_200 refers to. Some thoughts: I know that both the potential, and the periodic...
3. ### A Non interacting Fermions satisfy the Pauli exclusion principle

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...
4. ### Free electron model (Sommerfeld model)

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...
5. ### I Average energy of the electrons at T = 0

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.
6. ### Perturbation matrix: free electron model on a square lattice

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) >...
7. ### I Basic band theory question, free electron model

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...
8. ### Nearly free electron model: band gap

I was trying to determine the bandgap in the nearly free electron model. I'm having trouble to determine the band gap bewteen the second and the third band. Its a one dimensional problem. So, the central equation reads: ##\displaystyle \left [ \frac{\hbar}{2m} (k-G)^2-E \right ]c_{k-G}+...
9. ### What Causes the Forbidden Gap in Semiconductors?

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?
10. ### 2D problem of nearly free electron model

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...
11. ### Dispersion relation for the free electron model

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...
12. ### Nearly free electron model - band gap

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...
13. ### Programming the Nearly Free Electron Model Band Diagram for BCC and FC

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
14. ### Meaning of soulution of Central Equation: Nearly free electron model

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...
15. ### The free electron model vs. nearly free electron model.

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...
16. ### Comparing Silver Electron Spacing & Free-Electron Model

Homework Statement Compare the electron spacing of silver (0.26 nm) to the estimate for mean free path calculated earlier (52 nm), explain the discrepancy in terms of Pauli's free-electron model of conductivity. Homework Equations The Attempt at a Solution I would say this is down...
17. ### Free Electron Model: Exploring Differences with Plasma

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
18. ### Free Electron Model: Success & Metallic Density of States

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...
19. ### Solid State Physics - Free electron model

Homework Statement The following constant volume heat capacity data, Cv, were obtained for a 0.05kg sample of tin at low temperature. (The sample was maintained in the non-superconducting state by the application of a magnetic field). Assuming that tin obeys the Debye model of lattice...
20. ### The nearly free electron model and states in a band?

hi, I have this problem where I am supposed to show, using periodic boundary conditions, that there are 2N states in an energy band in the "nearly free electron" model of solids, where N is the number of atoms. I have been looking through my course notes and my textbook, and my textbook goes...
21. ### Free Electron Model: Why periodic boundary conditions and what is L ?

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...
22. ### Kittel nearly free electron model

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."...