-1
votes
1answer
26 views

Band structure and band index

Please let me know If my understanding is right. For a given $\vec{k}$, $H$ is a function of $\vec{k}$ the energies vary discretely for $n$ ie.,the band index. For a given $n$, we choose all the ...
-1
votes
0answers
29 views

Density of States of Free Particle in One Dimensions

I am using Quantum Mechanics by David H. McIntyre, chapter. This is problem 15.7: Find the density of states $g(E)$ for the case of a free particle in one dimension; further, show that the density of ...
-1
votes
0answers
15 views

A problem concerning the calculation of parameters in a periodic system [closed]

I am using Quantum Mechanics by David H. McIntyre, chapter 15. The question is 15.8: Find the single bound state energy of an electron in an isolated well of depth $V_{0} = 1$ eV and with width $b = ...
1
vote
0answers
50 views

Ion-neutralization processes and its energies

Ionization energies/Electron affinities are well mapped. I wonder about opposite processes... I imagine for anion the necessary energy will be equal to the electron affinity (energy released when ...
0
votes
0answers
28 views

band gaps in tight binding model

What happens at the zone boundaries of the brillouin zones in the tight binding model? How does the band gap originate in the TB model?
1
vote
0answers
19 views

Uncertainty principle characterizing metallic bonding?

So I was trying to think through the statement that the uncertainty principle can characterize metallic bonding. I know that the uncertainty principle is: $\Delta p \Delta x = \frac{\hbar}{2}$. And ...
1
vote
0answers
61 views

Variational principle

In the LMTO method, the interstitial region is approximated by plane waves and the muffin tin region of the potential by solutions to the radial Schrodinger equation. In using the variational method ...
0
votes
2answers
41 views

Why does chemical potential smaller than zero mean nondegeneracy and vice versa

In Mudelung's book, Introduction to Solid-State Theory, I have a confusion about the statement. Here, $x$ should be $\frac{\mu}{k_B T}$. I am cofused about his statement. Why does $x<0$ mean ...
3
votes
2answers
169 views

Why does $c_{-k,-\sigma}$ create a particle with momentum $k$?

In Mudelung's book, Introduction to Solid-State Theory, I am confused by the following statement. For many applications a further simplification is helpful. The concept of the hole presents us ...
2
votes
0answers
58 views

Derivation of existence of energy band gap in semiconductor (solid State)

I am looking for both a mathematical and a physical reason for energy band gap in metals. For Physical reason, I was told that at each reciprocal lattice, you could have Bragg scattering, that would ...
0
votes
1answer
37 views

What is the significance of the difference in the eigenvalue equations of Bloch functions for electrons vs photons?

any text on photonic crystals will highlight the almost perfect analogy between electrons in a periodic potential and photons in a periodic dielectric. The analogies are: $$V(\vec r + \vec R) = ...
3
votes
0answers
32 views

Separating the hamiltonian for a superlattice — is it this easy?

I've been banging my head against a wall trying to figure out what I'm sure is a very simple problem. I want to solve the Kronig Penney model for a superlattice, which is just a normal periodic 1D ...
1
vote
2answers
169 views

Dispersion Relation (e vs. k) clarification (crystal momentum or electron momentum)

If we get the dispersion relation from the Fourier transform of the lattice vectors then how do we get electrons information? Specifically, for the $k=0$ point of the graph, does this mean the ...
2
votes
2answers
133 views

A conceptual question about Green's function's treatment of interaction

Here we have electron gas and some other stuff. We expand the Hamiltonian to the 1st order of one single harmonic oscillator's displacement $\vec{u}$. Its equilibrium position is at the origin. Then ...
0
votes
2answers
64 views

Is crystal momentum an operator?

My teacher has for Bloch waves the notation $\langle \vec{r}|\vec{k} \rangle = e^{i\vec{k}\cdot \vec{r}}u_{\vec{k}}(r)$ and uses it consistently. However, does this not assume that there is an ...
0
votes
0answers
21 views

Is there a generic term for orbital groups such as $e_g$ and $t_{2g}$?

I am looking for a generic term for sets of atomic orbitals (viz. spherical harmonics) which are grouped by crystal symmetry. The most familiar examples would be $e_g$ and $t_{2g}$ (in cubic ...
1
vote
1answer
86 views

When can i separate spin from the wavefunction?

I am currently working on a Tight-Binding model and for the derivation of nearest neighbor spin interactions I have terms like $$ ...
3
votes
1answer
114 views

Group analysis forbids band-crossing in 1D?

Group analysis forbids band-crossing in 1D in terms of conventional band theory. I read this in a good solid state physics book. But there's no explanation at all. Can anyone help on this?
3
votes
3answers
105 views

Why can we quantize macro(meso)scopic harmonic oscillator?

It is well known that we have got many kinds of quantized macro(meso)scopic harmonic oscillators or so in tiny mechanical systems. People are talking about cavity cooling and so on. However, it is ...
0
votes
1answer
116 views

Overview and doubts about Bloch's theorem and the concept of partial density of states

So I have a large confusion with QM as applied to solid state. The following is a summary of what I know, what I think I know, and what I know I don't know. I hope to stir a discussion that will help ...
1
vote
1answer
83 views

Density of states (treating states in continuum)

If we have a particle in a 3D infinite square well box, with length $L$, e.g. an electron in a conduction metal. By solving the Time independent Schrodinger equation, we can get the formula of ...
2
votes
2answers
232 views

How to interpret band structures

I'm currently taking a Solid State Physics class, and is currently reading about the quantum mechanical description of solids. I then came across the following figure: It's supposed to be the band ...
1
vote
1answer
48 views

Possibility of stable muonic structures?

In an analogy to the neutron, which decays rapidly as a free particle, but when bound in a nucleus it is stable, would it be possible to crease a structure that permits the stability of muons - be it ...
1
vote
2answers
126 views

Bloch wave function orthonormality?

there is this text book that is giving me a hard time for a while now: It shows that Bloch wave functions can be written as $$\Psi_{n\vec{k}}\left(\vec{r}\right) = \frac{1}{\sqrt{V}}e^{i\vec k \vec ...
0
votes
0answers
97 views

Interpreting a Hamiltonian in terms of 'hopping' operators

I am having some trouble interpreting a Hamiltonian in terms of "hopping" operators. The Huckel model for nearest neighbour interaction in graphene is given by $$H=-t\sum_\vec{R}|\vec ...
2
votes
2answers
541 views

Determining if a semiconductor is n-type, p-type or intrinsic

The probability that an energy state in the conduction band is occupied by an electron is 0.001. Would this semiconductor then be n-type, p-type, or intrinsic? Notation that I use: $E_F$ represents ...
0
votes
1answer
98 views

Photoelectric effect high frequency limit?

The photoelectric effect has a low frequency limit below which nothing is observed. Increasing the frequency energy is enough to free an electron. Continuing to increase the frequency the material ...
2
votes
1answer
309 views

Derivation of Matrix Components of Hamiltonian in Tight Binding Method

Im currently struggling with the description of the tight binding method in the original paper by Slater and Koster from 1954 (where a free version of the paper can be found under this link). In ...
2
votes
1answer
140 views

Connecting Fermi levels and band diagrams to potential diagrams?

I'm trying to make sense of how you can find the potential diagram given the band diagrams of a few adjacent materials. As a simple example, in semiconducting heterostructures, if you have sandwich ...
3
votes
2answers
350 views

Need help understanding Semiconductor physics

I am trying to read Kittel for a project, and he mentions the properties on silicon and germanium so briefly, that I don't understand it at all. He talks about p states, and I don't really know what ...
0
votes
1answer
295 views

Perturbation theory

I am puzzled with perturbation theory when studying quantum mechanics and solid theory. What I learn about perturbation is, from my ignorant point of view, just mathematics, or even simpler, matrix ...
1
vote
0answers
87 views

Equal time displacement correlation functions and their physical interpretation?

Displacement correlation functions in question are within harmonic approximation and are derived for example in: A. Maradudin, Dynamical properties of solids 1, 1 (1974). Maradudin says about the ...
5
votes
1answer
63 views

Meaning of the 'deep lattice limit' and 'shallow lattice limit'?

In condensed matter literature, at many places, the phrase 'deep lattice limit' is used. Please tell what is the deep lattice limit and the shallow lattice limit?
0
votes
1answer
434 views

Bound states and scattering length

What is the relationship between bound states and scattering length? What is the relationship between scattering states and scattering length? When we say, potential is 'like' repulsive for ...
1
vote
2answers
327 views

Particle current operator in general vs Particle current operator for tight binding Hamiltonian

I am referring Mahan Many-Particle Physics. There are 2 particle current operators -one in general and one for the tight binding Hamiltonian. How do we go from the general current operator (1.195 in ...
2
votes
2answers
313 views

Sign of the hopping integral in tight binding model

The Hamiltonian of tight binding model reads $H=-|t|\sum\limits_{<i,j>}c_i^{\dagger}c_j+h.c.$, why is there a negative sign in the hopping term?
6
votes
2answers
276 views

Change of basis in non-linear Schrodinger equation

At the mean-field level, the dynamics of a polariton condensate can be described by a type of nonlinear Schrodinger equation (Gross-Pitaevskii-type), for a classical (complex-number) wavefunction ...
1
vote
1answer
155 views

What is paramagnetic current-current correlation?

I know what paramagnetism is. But first I want to know about the paramagnetic current and then the above-mentioned correlation? Actually, I am working on a paper on superconductivity where I have ...
5
votes
2answers
427 views

What prevents bosons from occupying the same location?

The Pauli exclusion principle states that no two fermions can share identical quantum states. Bosons, one the other hand, face no such prohibition. This allows multiple bosons to essentially occupy ...
1
vote
2answers
171 views

Eigenfunctions in periodic potential

For Hamiltonian $\operatorname H$ and lattice translation operator $\operatorname T$, if $$\operatorname H\psi=E\psi, \qquad \operatorname T\psi=e^{ik\cdot R}\psi,$$ and $$\operatorname ...
3
votes
1answer
343 views

Does a quantum phase transition have latent heat?

As the title says, I am thinking about the question that whether a quantum phase transition has latent heat. If so, at 0 temperature, we can drive the system by some parameter from disorder phase to ...
5
votes
2answers
1k views

What is the difference between a photon and a phonon?

More specifically, how does a wave-particle duality differ from a quasiparticle/collective excitation? What makes a photon a gauge boson and a phonon a Nambu–Goldstone boson?
7
votes
1answer
232 views

Simulating the evolution of a wavepacket through a crystal lattice

I am interested simulating the evolution of an electronic wave packet through a crystal lattice which does not exhibit perfect translational symmetry. Specifically, in the Hamiltonian below, the ...
2
votes
0answers
93 views

What is Z3 exciton?

I am searching and studying excitons and I confronted with a term named Z3 exciton. What is it? And what is its difference with, for instance Z1 or Z2 exciton?
0
votes
1answer
107 views

Characteristics of bloch electron in a priodic potential

Effective mass of a Bloch electron in a periodic potential is negative why ?
5
votes
1answer
129 views

Order of magnetic phase transitions

Is there any phase transition occur in paramagnetism to diamagnetism transitions state. What should be the order and how will I calculate the order?
9
votes
3answers
445 views

Derivation of the “Bethe sum rule”

I am trying to work out the steps of the proof of the expression: $$\sum_n (\mathcal{E_n}-\mathcal{E_s})|\langle n|e^{i\mathbf{q}\cdot\mathbf{r}}|s \rangle|^2 = \frac{\hbar^2q^2}{2m}$$ from Eq. (5.48) ...
2
votes
1answer
455 views

What is different between resolvent and green function

I bumped into a book, where Resolvent $R^{\pm}(E)$ is defined as $e^{\mp iHt/\hbar}=\pm\frac{i}{2\pi}\int_{-\infty}^{\infty}dER^{\pm}(E)e^{\mp iEt/\hbar}$ and $R^{\pm}(E)=\frac{1}{\pm ...
1
vote
1answer
268 views

Why do the drift and diffusion components cancel for each type of carrier if EHP generation plays such big role in p-n-junctions?

I have always argued to myself that drift and diffusion components of the current though a p-n-junction cancel for each type of carrier because any electron diffusing from n into p will sooner or ...
2
votes
2answers
491 views

How robust is Kramers degeneracy in real material?

Kramers theorem rely on odd total number of electrons. In reality, total number of electrons is about 10^23. Can those electrons be so smart to count the total number precisely and decide to form ...