Statistical Definition and 582 Threads

Homework Statement Give the number of states (energy of the state smaller than E<0) \Phi(E) of a spinless particle with mass m in the central potential V(\vec{r})=-\frac{a}{\left|\vec{r}\right|}. Homework Equations The Attempt at a Solution Hi, the hamiltonian of this problem...

I have some questions that my teacher was unable (and unwilling) to answer in class, so I thought I'd ask them here. The chemical potential \mu=\left(\frac{\partial U}{\partial N}\right)_{S,V} is given by the derivative of the energy with respect to particle number at constant volume and...

Homework Statement In a system of N weakly interacting particles each particle can be in one of M energy states: E_1 < E_2 < ... < E_M At T=300K there are 3 times as many particles in E_2 as in E_1. Calculate E_2 - E_1 Homework Equations This is not my homework, just a tutorial question, I'm...

Does anyone have any recommendations of a good book(s) for a first undergraduate-level course in Statistical Mechanics?

I took stat mech as an undergrad but the textbook we used (statistical and thermal physics by sturge) was over my head. Can someone provide a good and readable (as readable as stat mech can get) textbook for stat mech? I am switching to a different research group in grad school that deals with...

When I learned statistical mechanics, it followed the lines of the maximum entropy principle from information theory as laid out by Jaynes which can also be seen as a Bayesian statistical theory. I wonder whether there exist some orthodox frequentistic interpretation of statistical mechanics...

I was thinking of taking the statistical mechanics course for PhD candidates that's being offered next term at my school. My background is pretty typical, I've had Calc 1-3, linear algebra, differential equations, classical mechanics, e&m, thermodynamics with statistical mechanics, all at the...

How do you use the C_ij matrix to find the harmonic frequency (or frequencies) of a diatomic molecule, the OH (hydroxyl) radical? (I have no idea how to set it up for this.) This is from Feynmann's book on Statistical Mechanics...

Homework Statement a) Derive an asymptotic expression for the number of ways in which a given energy E can be distributed among a set of N, one-dimensional harmonic oscillators, the energy eigenvalues of the oscillators being (N+\frac{1}{2})\hbar\omega, n=0, 1, 2, .... b)Find the corresponding...

Statistical Thermodynamics - Help Wanted :( (My translation skills sucks, I hope it is understandable.) Three spins, placed at vertices of an equilateral triangle, are put in the external magnetic field with density B. Hamiltonian of the system: H = -J \sum_{<i,j>} s_{i} s_{j} - \gamma...

Hi, i'm an Applied Physics student (2nd year). Could you please tell me a book to study thermodynamics from? I've studied from Thermodynamics, Kinetic Theory, and Statistical Thermodynamics by Sears - Salinger and it is pretty good. Has anyone "tested" : 1) An Introduction to Thermal Physics by...

Homework Statement Consider a particle confined within a box in the shape of a cube of edges Lx=Ly=Lz. The possible energy levels of this particle are then given by the quantized energy for a particle in a 3D box. Calculate explicitly the force per unit area (or pressure) on this wall...

Homework Statement Consider a particle confined within a box in the shape of a cube of edges Lx=Ly=Lz. (a) Suppose that the partice is in a given state specified by particular values of the principal quantum numbers nx, ny, nz. By considering how the energy of this state must change when...

I was looking at a derivation of entropy expressed as an absolute probability: S = -k. SUM P.lnP (What is the name of this by the way?) In the derivation, it makes the following statements which I really just don't get! U = SUM E.P so therefore dU = SUM E.dP - SUM P.dE Where does...

I am currently enrolled in PHY4523 - Thermodynamics and Statistical Mechanics where we are currently using "Fundamentals of Statistical and Thermal Physics" by F. Reif and I was wondering if there were any good recommendations as far as supplemental texts that I could use in helping me...

Homework Statement From Landau and Lifgarbagez: \langle (\Delta f)^{2} \rangle = \overline{f^{2}} - (\overline{f})^{2} This isn't derived, just stated, and I'd like to understand how it comes about. f is a generic quantity "relating to a macroscopic body or to a part of it."...

I posted this once already without seeing the rule that HW questions must go here--sorry :redface: So, the problem: I'm really lost on where to get started here. It's a two state system, one with energy 0 and the other with energy ε. I already have ensemble average, <E>, found to be: ε / (e^βε...

I'm really lost on where to get started here. It's a two state system, one with energy 0 and the other with energy ε. I already have ensemble average, <E>, found to be: ε / (e^βε + 1) , where β is thermodynamic beta, 1/KbT. How do I convert this to an expression for the variance of the...

Hello there, I'm a second year physics student who like most, has exams around the start of the next year and as such, have started revising for my exams. The term has introduced new physics I wasn't initially familiar with such as Quantum mechanics and advanced differential calculus. Another...

Hi all, I'm looking for a rigorous (in a mathematical sense) treatment of statistical thermodynamics. I'm at the tail end of a class on stat thermo that used the book by Bowley and Sanchez. This book is not what I'm looking for. Does anyone have any suggestions?

So I didn't start my physics major until my sophomore year which means I'm a year behind. Because of this I won't be able to take quantum mechanics until the first semester of my senior year which is also when statistical mechanics is offered. I'd really like to take statistical mechanics but...

Hi, Could anyone tell me what type of statistical test is used to estimate the parameters of the standard model? I hear many particle physicists say, eg. "we have a 95% confidence that this quark mass falls between A and B" and what immediately comes to mind are the methods of statistical...

Sorry for a (maybe) dumb question, but... I understand that according to QM, the description of the situation for a particle or system is described by a linear superposition of the wave functions of all the possible states (eigenstates) of the system. When a measurement is made, the wave...

Consider an ideal gas of oxygen atoms in equilibrium with oxygen atoms absorbed on a planar surface. here are N_s sites per unit surface area at which the atoms can be absorbed, and the energy of an absorbed atom is -e compared to one in the free state. The system is under 1 atm and at 300K...

I am quite well versed with the random walk problem and am interested in finding out more about Brownian motion. Does anyone have any suggestions for books that explain Brownian motion in detail? I suspect these will be books on statistical mechanics.

Hi! I'm a graduate student in solid state physics and I have to follow a graduate course on equilibrium statistical physics, and we're using Plischke and Bergersen's book on "Equilibirum Statistical Physics". Presently, we're seeing Mean Field Theories and Ising model, but somehow, I'm not...

Hi there, I'm searching for a good book for statistical physics. Professor as told us that the bibliography was Reif or Kittel (thermal physics) However, both are a little bit old, and some not very formal. I'm wondering if something more formal, more recent, with more or less the same...

Given a macro-state M of a system, let S denote the potion of the phase space that has the macro-state M. A micro-canonical ensemble is one in which the probability of finding the micro-state in any part of S is equally likely (the density function is constant over S). In Pathria's...

Hello, In some applications, statistical averages are encountered in the derivation of system models. Practically, how can we find the statistical average? Is there mathematical expression to express the expected value? Thanks in advance

I'm not sure if this is the proper location for this thread, but its for a math course and I think my issues concern the math portion of the problems. If it should be moved please do so. Note: I know the post is quite long, so I'll just pull out my few main issues from all the junk. 1)...

I've been refreshing myself on some of the statistical mechanics I learned a couple years ago, using Kittel and Kroemer as a guide. However, I've come across a couple things that bother me: 1. When the Boltzmann distribution is derived, no real physics enters the picture. Essentially, the...

Hi guys, I am reading Reif's book on statistical mechanics and have a question on the H theorem. In section 2.3, Reif gives (on page 54) both the definition of equilibrium as well as a fundamental postulate. Definition: "An equilibrium situation is characterized by the fact that the...

I'm an ME grad student in the thermal fluids area and a lot of my work involves electrochemistry, a little bit of inorganic chemistry, and optics, along with fluid and energy transport (fuel cells and stuff). I'm considering taking a statical thermodynamics class this fall to help me better...

Recently I was asked whether the concept of a statistical ensemble is actually realistic and I recognized that I can not really answer this question myself. I think that it is more a mathematical "tool", because of the probability nature rather than a realistic "thing", but still it helps us to...

So, I am working with a professor on some astronomy research. I need two compare two samples but one of them has a much smaller size due to the lack of observations. The samples have about 5 parameters. I don't know much about statistics but from reading so far I think the...

I need a statistics book to help me understand concepts like skewness and kurtosis. I don't need a really advanced book, just one that will hopefully give me an understanding about the topics and make me able to implement them on my own. I have very little background statistics or probability...

Hello, in statistics, one can derive the moments of a distribution by using a generating function <x^n> = \int dx x^n f(x) = \left( \frac {d}{dt} \int dx \exp(tx) f(x) \right)_{t=0} = \left( \frac d {dt} M(t) \right)_{t=0} Is there a similar method to derive the multipole moments in...

I am not sure how to answer the following question, which I have posed to myself to better understand the method: "Suppose two six-sided dice are rolled together N times. What is the uncertainty in the number of times any given total appears on the dice?" For example, what is the...

I'm new here, so first of all Hi :) I did some reading & searching but didn't find an answer direct enough to the issue that bothers me: there's something regarding the power of a statistical test, 1 minus beta, that doesn't add up for me. I'd appreciate any assistance, and if it's possible...

I have of late been reflecting on something. Generally as a rough approximation we may divide physics into classical mechanics, quantum mechanics, classical field theory (like E/M, fluid mechanics...), quantum field theory, and then statistical mechanics. All the classical and quantum...

Does fact that QFT in imaginary time is equivalent to QSP represents the proof that many-particle quantum physics is equivalent to quantum theory of fields? To elaborate a little, I had some discussion with some engineers, and when I was explaining them Standard Model I had to invoke concepts...

1. Homework Statement [/b] There are N 3-dimensional quantum harmonic oscillators, so the energy for each one is: E_i = \hbar \omega (\frac{1}{2} + n_x^i + n_y^i + n_z^i). What is the total number of states from energy E_0 to E, and what is the density of states for E? The Attempt at a...

Homework Statement Consider a system of 8 one-dimensionaly harmonic oscillators. Initially this system has 3 quanta of energy. Byhow much does the entropy change if you add one more quanta of energy? Homework Equations S=k*ln(omega) omega=(q+N-1)!/(q!*(N-1)!) The Attempt at a Solution...

I am currently trying to get my head round RG in the context of statistical mechanics and am not succeeding! I would be grateful for any help. I have a specific question, but any clarification of RG in general would be useful. Here is my understanding of the main ideas: 1. Define...

I have my main UG exam on Sat & i dnt have answer to these questions . Help me out Q. Distinguish b/w degenerate energy level & a degenerate gas ? Ans : Degenrate level : A single energy level can be degenerate with another energy level , no difference b/w their energies . Degenerate...

Homework Statement N weakly interacting distinguishable particles are in a box of volume V. A particle can lie on one of the M possible locations on the surface of the box and the number of states available to each particle not on the surface (in the gas phase) is aV, for some constant a. 1...

I've recently bought the 1965 copy of the reif textbook by mcgraw hill, fundamentals of statistical and thermal physics. The book seems like it is an advance level book. Anybody have any feedbacks about this textbook? Also, are there newer versions of this book?y 1965?

Homework Statement One class application of correlation and regression involves the association between the temperature and the number of times cricket chirps in a minute. Listed below are numbers of chirps in 1 minute and the corresponding temperature in degrees Fahrenheit. Chirps in 1...

For some given statistics (e.g. Fermi-Dirac or Bose-Einstein), once we know the average number of particles at state r, it is easy to calculate the dispersion by calculating \overline{(\Delta n_r)^2} = -\frac{1}{\beta}\frac{\partial \bar{n}_r}{\partial \epsilon_r} and the total number of...

I took classical (engineering) thermodynamics a few years ago, and this semester I am taking a statistical thermodynamics class from the physics department. We are using the book "Fundamentals of statistical and thermal physics" by Reif, which seems to be a pretty good book. Unfortunately I...