Landau Definition and 115 Threads

I just decided to look at Landau & Lifshitz' Classical Theory of Fields (English version, 4th ed), and I am a bit embarrassed to be confused already on page 4&5 of this book. The book can be viewed on archive.org. The goal of this section of the book is to show ##s = s'## starting from only the...

I feel like I might be posting many questions, so I hope you're not angry with me on this. I'm following Landau's book and try to understand why L = K - U but first we need to figure out why it contains K. Landau discusses two inertial frames where the speed of one frame relative to another is...

Trying to grasp the Landau's book and struggling here. (Attaching the image).If you multiply L by some constant and put it in in the Euler-Lagrange equation, motion equation won't be changed. Q1: Though, what does he base his logic to say ##Lim L = L_A + L_B##. If we got 2 separated system, he...

I am a beginning graduate student and I've been assigned a paper which uses landau levels for 3d fermionic gas in uniform background magnetic field. I am having trouble finding a proper source which deals with solution of dirac equation in such a case. With the two papers that i have found which...

At non-relativistic limit, m>>p so let p=0 At non-relativistic limit m>>w, So factorise out m^2 from the square root to get: m*sqrt(1+2w(n+1/2)/m) Taylor expansion identity for sqrt(1+x) for small x gives: E=m+w(n+1/2) but it should equal E=p^2/2m +w(n+1/2), so how does m transform into p^2/2m?

Hello there, for the above problem the wavefunctions can be shown to be: $$\psi_{n,l}=\left[ \frac {b}{2\pi l_b^2} \frac{n!}{2^l(n+l)!}\right]^{\frac12} \exp{(-il\theta - \frac {r^2\sqrt{b}}{4l_b^2})} \left( \frac {r\sqrt{b}}{l_b}\right)^lL_n^l(\frac {r^2b}{4l_b^2})$$ Here ##b = \sqrt{1 +...

Hi all, I am somewhat familiar the Landau Ginzburg paradigm for phase transition. My understanding is that it is a phenomological model of 2nd order phase transitions by "guessing" that the free energy can be expanded a configuration integral (path integral) of a functional of a local order...

So for part a, I separately minimized F wrt ##\theta## and ##P## and got the following. $$\frac {\partial f} {\partial \theta} = a_{\theta}(T-T_{\theta})\theta + b_{\theta}\theta^3 - tP = 0$$ $$ \frac {\partial f} {\partial P} = \alpha(T-T_P)P -t\theta$$ $$ P = t\theta \alpha (T-T_P) $$ Then...

I actually have worked through the solution just fine by taking the derivative of \vec{L}: \frac{d \vec{L}}{dt} = \dot{\vec{v}} \times \vec{M} - \alpha \left(\frac{\vec{v}}{r} - \frac{\left(\vec{v} \cdot \vec{r}\right)\vec{r}}{r^{3}}\right) I permuted the double cross product: \dot{\vec{v}}...

Hello : i am reading now landau & lifshitz book on mechanics and i have small question : about L(v^2) notation it was not very clear in the book and i couldn't understand it correctly anyone can explain it or provide a link with explanation page (4 - 5) Best regards Hagop

I have been struggling for over a month now with a problem I cannot fix. I would really appreciate any comment or guidance. Thank you! I am considering an Ising-like model with N agents that han hold one of the following 3 states, represented by vectors: state + : vector (1 0) state 0 : vector...

Let ##K## and ##K'## be two inertial frame, If K is moving with infinitesimal velocity relative to ##K'## , then ##v' = v + \epsilon##. Note that ##L(v^2) - L(v'^2)## is only a total derivative of a function of coordinate and time. (I understand this part) Because ##L' = L(v'^2) = L(v^2 +...

I understand that d/dv(L) = constant, and L is only dependent on v, but how do we get to the fact that v = constant?

Thanks in advance for any insight! Following Pathria's discussion of phase transitions, I'm getting tripped up on the discussion of Landau's theory. Pathria begins with a zero-field free energy ##\psi = A/NkT## where ##A## is the Helmholtz free energy. He proceeds to characterize the...

Dear PF, I hope I've formulated my question understandable enough. Thank you for your time, Garli

Hi all, I have some doubts regarding the Kolmogorov test: I made a simple c++ program generating two samples of random numbers following a Landau distribution (I used the "hit and miss" method). I made the Kolmogorov test, in order to check the randomness of the generator, but I'm having some...

Which textbook is better for an upper division course in classical mechanics - Goldstein’s book or L&L’s book?

I have no clear idea of this phenomenon?

Homework Statement A particle of mass m moving with velocity v1 leaves a half-space in which its porential energy is a constant U1 and enters another in which its potential energy is a different constant U2. Determine the change in the direction of motion of the particle. Homework Equations...

I've been told Landau damping was a surprising phenomenon that many people didn't believe possible when first introduced since it permit wave damping in the absence of collisions. I appear to be missing something fairly basic and fundamental to this picture, but aren't all wave-particle...

Related to Figure 8.4 the author mentions this when stating (8.25): "Note that the semi-circle deviates below the real -axis, rather than above, because the integral is calculated by letting the pole approach the axis from the upper half-plane in -space." Why is the pole calculated in this way...

I'm usually entirely autonomous in planning out my curriculum (and have read much great advice here in aid); but my physics curriculum is proving more difficult to plan out than my math curriculum. I was thinking as a start: Kleppner & Kolenkow Mechanics, Purcell Electricity and Magnetism, and...

I'm trying to understand cyclotron resonance measurements of electron effective mass in intrinsic silicon. I need to understand the theory used to make the computations of effective mass in non-parabolic bands. A basic introduction to the cyclotron technique is here, but only for parabolic...

Hi. I want to know about relativistic Landau levels (especially about massless Dirac fermion in a uniform magnetic field), but I cannot find textbooks. Does anyone know textbooks or articles about it? Thanks.

Homework Statement [/B] 1) Is the order paramter ##\phi(x)## intensive or extensive? 2) Is ##M## intensive or extensive? With the following definitions : Homework Equations The Attempt at a Solution 1) Free energy is extensive, however I don' think I can use this to deduce whether...

In the B level thread:..."how to change electron and proton charge"...it was claimed that "the closer you get to an electron the bigger the charge". This struck me as odd because I though that electron charge was a fundamental constant and so I asked for clarification. This was given but extra...

Currently I'm set to pursue solid state physics in a EE department, working on more practical theory. However I'm seeing a lot of papers studying mathematically obfuscatory topics such as topological materials, Berry's phase, quantum phase transitions, and other abstruse (albeit important and...

It seems Lev Landau created an entry exam to test his students, and the exam was known to be ridiculously hard. To get an idea as to how hard the test really was, I've been scouring the Internet for problems Landau proposed... so far I've managed to find only four. Electrodynamics A dielectric...

The Landau Lifshitz book "Mechanics" has a good reputation of one of the best books, not only on classical mechanics, but on theoretical physics in general. Yet, I have found a serious conceptual error (or at least sloppyness) in it. Sec. 23 - Oscillations of systems with more than one degree...

Homework Statement I am not sure whether the meaning of the equation ##(3)## which used for deriving momentum is as same as equation ##(4)##.I will make a detailed description below. The lagrangian function for a free particle is ##L=-mc^2\sqrt{1-\frac{v^2}{c^2}} \quad (1)## The action from...

Hi everyone, I am currently going through L&L slowly but surely (it's like 1 page Landau = 5 pages of notes/connections). I was wondering if anyone knew if there were any published errata for the series. Haven't found any in my Google searches. What I'm talking about is usually notational and...

I have been reading about Landau levels for a two-dimensional system of charged particles in a perpendicular magnetic field and I have trouble understanding why there is degeneracy in the system. Let me provide some background to my problem. In the presence of a magnetic field, the momentum of a...

Hi, in the case of free electrons gas under the effect of a magnetic field. The hamiltonian of an electron doesn't contain a term of Spin-Magnetic field interaction this means that it contains just the kinetic energy terms. Why is that ?

Hello. In my university the course of the Field theory was based on Landau's book, which of course, is a quiet rough book to introduce a subject with - so all I was left with was superficial knowledge of the branch. I would like to read another book (introductory level is preferred) about the...

Book: Landau Lifshitz, The Classical Theorey of Fields, chapter 11, section 95. I have gone through the derivation of Einstein field equations but not without holes to fill and fix in my understanding. Let's start with the action for the grtavitational field ##S_g## which after some explanation...

<<Mentor's note: this is spin-off this thread>> One error I'm aware of in LL vol. I is the claim on integrability. But what's wrong with LL's treatment of anholonomous constraints (in sectin 38 in my German edition)? It just leads to the usual equations with Lagrange parameters you also get...

Hello, I'm sure most of you are already familiar with the book "Mechanics" by Landau and Lifshitz. There's a section that I do not understand. In section 4 towards the end they mentions that "It is easy to see that the mass of the particle cannot be negative." They then give the argument that...

Homework Statement Define n=(x + iy)/(2)½L and ñ=(x - iy)/(2)½L. Also, ∂n = L(∂x - i ∂y)/(2)½ and ∂ñ = L(∂x + i ∂y)/(2)½. with ∂n=∂/∂n, ∂x=∂/∂x, ∂y=∂/∂y, and L being the magnetic length. a=(1/2)ñ+∂n and a†=(1/2)n -∂ñ a and a† are the lowering and raising operators of quantum mechanics. Show...

I have starting working through section 134 of Landau and Lifshitz, vol 6, and it seems I have entered some kind of twilight zone where all my math/physics skills have left me :cry: The derivation starts with the energy-momentum tensor for an ideal fluid: ## T^{ik} = wu^i u^k - p g^{ik} ##...

If suppose only if the velocities are determined for all N particles can the system be completely determined, can we not extend and say that only if acceleration for all particles are provided can the system be completely determined? For instance can there not be two systems of N particles with...

Landau level is the energy levels of free electron gas in a magnetic field. However, this term is also frequently used in solid state physics. I have the following questions: 1. what does this term exactly mean in band theory? After all, electrons are not free here. 2. why is de Haas-van Alphen...

Hello,i am just starting to learn Quantum Mechanics in the university at an underdrad level. I know there are a lot of great introductory books out there but i just saw that Landau's book on non-relativistic quantum mechanics has great reviews but upon seeing it,i was overwhelmed by the...

Homework Statement A simple model for liquid crystals confined to 2 dimensions is o assume each molecule can only align in one of 2 perpendicular directions. To construct a landau model its convenient to define order parameter, s : s = 2 ( Np - 0.5Nt ) / Nt Np - number molecules...

Hello, PF, I'm going to be taking graduate CM next semester and the professor uses Landau's textbook instead of Goldstein, which I take is the usual text. What are the appreciable differences between the books and what kind of math will be needed? I have the basics-complex analysis, linear...

Homework Statement Consider the Landau free energy ##\mathcal{L}=-hm+r_1 t m^2+Cm^3+s_0 m^4## with an additional ##m^3## term. We consider zero magnetic field case ##h=0## and ##s_0>0##. a.) Please show that there are two critical temperatures ##t*## and ##t_1##. When ##t<t*##, a second...

Consider an Ising model system where the total energy is ##E = −J \sum_{<ij>} S_iS_j ##, ##S_i = \pm 1## and ##< ij >## implies sum over nearest neighbours. For ##J < 0## the ground state of this system at ##T = 0## is antiferromagnetic. (All adjacent spins misaligned so net magnetisation zero...

Homework Statement The total energy of the Ising model is ##E = −J \sum_{<ij>} S_iS_j ##, where ##S_i = \pm 1## and ##< ij >## implies sum over nearest neighbours. For ##J < 0## explain why the ground state of this system at ##T = 0## is antiferromagnetic. Let ##m_{1,2}## be the magnetisations...

I wasn't really sure where to post this, and while the answer might seem obvious (he simply didn't write it) it just seems odd. The title of the book is still Landau Lifshitz Course for Theoretical Physics, and its technically his series, but vol 4 (QED) is authored by Lifshitz, Pitaevskii and...

This question is about the Landau Ginzburg of phase transitions which seem to take this classical field theory form. I don't understand the meaning of the 2nd to last equation $$b(T) = b'(T -T_c) $$ does that mean b(T) has be redefined in the previous two equations relative to the original...

Which books can be considerd classics in the field of quantum mechanics (I am talking about books like Balletine, Landau and so on)?