Statistical Definition and 582 Threads

Homework Statement If ##Z## is homogeneous function with property ##Z(\alpha T,\alpha^{-\frac{3}{\nu}}V,N)## and you calculate Z(T,V,N). Could you calculate directly ##Z(\alpha T,\alpha^{-\frac{3}{\nu}}V,N)##. Homework Equations ##Z(T,V,N)=\frac{1}{h^{3N}N!}(2\pi m k...

Hi all, quick query please: My nearest university is a good one (with a good department) but offers only an MSc Mathematics, not an MSc Statistics. But the course options are such that it can be virtually all statistics and probability. E.g. modules include Mathematical Biology, Medical...

I've been reading, in my own time, a first course in thermodynamics and they present a quantum treatment of statistical mechanics (discrete energy levels), but on the article for the partition function on wikipedia, I find out that there is a classical treatment of statistical mechanics as well...

The probabilistic nature of QM seems apparent(in theoretical formulation as well as experimentally), then why do most of the physicists give the credit of in-determinism to the nature itself and look for many worlds, abruptly collapsing observer conscious experiment setups, and the likes...

That's the only equation I know on the topic so far. I'm an undergrad physics major and one of my courses this term is statistical mechanics which I am finding to be overwhelmingly difficult to understand. Apparently the course is considered "graduate level," although they still require us to...

I was studying statistical mechanics and found some concept that are difficult for me to grasp. Any kind of help will be highly appreciated. My questions are : 1. In equilibrium which quantity should be maximized? Is it the number of Microstate or the way that a particular Microstate is...

Homework Statement A system of N particles has three possible energy levels namely; 0, E and 4E. How many particles does one expect in the second state at temperature T? Homework Equations It's a sample problem for our finals. Our Text book is Statistical Mechanics by Roger Bowley and...

So, there are two things in Quantum Mechanics that I understand are axioms: the first is the schrodinger equation, which cannot be derived. Okay fine, we have to start somewhere. The second axiom is that the integral from a to b of the wavefunction-mod-squared gives the probability of finding...

Hello. I developed an algorithm to detect events in time domain and I want to know the efficiency of the algorithm. The problem is related with the time duration of the data. Each file has data with a time duration of hundreds of minutes and I have dozens of files. Instead of...

Hello, Trying to make sense of the odds that I (or you) exist, from what I read people say its basically 0, which doesn't make sense to me since I am here after a short ~14 billion years of our universe existing. Given IF the universe and time are infinite, my odds of existing again, no...

Homework Statement A polymer consits of ##10^{20}## monomers, each 2 nm long. One end of the polymer is hanged at the ceiling on the other end, we have a load of ##4\cdot 10^{-10}g##. Calculate the average potential energy!Homework Equations The Attempt at a Solution Well... I don't know...

Homework Statement A system of N distinguishable particles is arranged such that each particle can exist in one of the two states: one has energy \epsilon_{1}, the other has energy \epsilon_{2}. The populations of these states are n_{1} and n_{2} respectively, (N = n_{1}+n_{2}). The system is...

Hi, I'm completely lost in this discipline. Does anyone know of a good book with solved exercises and some examples, particularly on the 3 types of ensembles (microcanonical, canonical and large canonical), quantum mechanics statistical physics, and fermions/bosons gases? Thank you.

We don't have rigorous approach to statistical mechanics but have an intuitive one.We follow Concepts of Modern Physics by Sir Arthur Beiser. It is given that n(ε)=g(ε)f(ε) Here ε is the energy state. where according to my understanding n(ε)=number of particles which are present in an...

I am planing to study thermal physics on my own as I got an incompetent faculty who doesn't know anything about this subject. I want to have a detailed understanding about the topic. So can somebody suggest me which book I should follow from the following list. 1. Schroeder, Thermal...

I'm taking stat mech right now (Kittel book) and...I might hate it. I love e&m, quantum, classical, relativity, but I like almost none of what we're doing in this class. It's not the type of physics I'm interested in and it's abstract in a way I don't like (I normally like abstraction). I know...

Homework Statement There are 5 Bosonic particles N = 5 populating 2 degenerate energy levels E1 and E2 such that: E1 < E2, N2 ≤ N1 and the respective statistical weights are g1 = 3 and g2 = 2. . What are the possible macrostates of this system?The Attempt at a SolutionI'm not sure if the...

I am supposed to do an experimental report in my Social Psychology class. I am analyzing the factors affecting the lack of females in engineering and other math-intensive fields. I measured men and women's life interests, life values and attitudes to gender roles in our survey because I think...

Prove that the following two statements of the second law are equivalent (each one can be derived from the other): (a) “It is impossible for heat to flow spontaneously from a colder to a warmer body without causing other changes” (b) “It is impossible to convert all the heat taken from a...

Usually in the problems I have done, I found the partition function by simply summing exponential of the eigenenergies, but lately I have started to wonder why this approach is correct. Do we not want to sum over the energies of all possible states as we did in the classical case. In that case...

Could someone explain what this branch of physics encompasses? Is it just using statistics and probabilities to explain phenomena?

I'm taking Stat Mech at the graduate level and I find the course incredibly frustrating in that it just feels like a whole lot of mathematical formalism without any examples. I've looked in Paritha, Huang, and Salinas and all these books seem the same in that they just looks like a bunch of...

Homework Statement Consider two spin-1/2 subsystems with identical magnetic moments (μ) in equal fields (B). The first subsystem has a total of NA spins with initially "a" having magnetic moments pointing against the field and (NA - a) pointing along the field, so that its initial energy is...

A glass bulb contains air at room temperature and at a pressure of 1 atmosphere. It is placed in a chamber filled with helium gas at 1 atmosphere and at a room temperature. A few months later, the experimenter happens to read in a journal article that the particular glass of which the bulb is...

Please help me, what are micro and macrostates, what are accessible states?

An Introduction To Thermodynamics And Statistical Mechanics by Stowe is the course textbook for my Statistical Physics course I am having trouble with the book as it does NOT provide good examples and explanations nor does it have solutions just answers. I was wondering if there is Schaums or...

In a aislate system, the probability on a microcanonical state \Gamma is p(\Gamma ) = 1/K , if E<H<E + ΔE, and 0 on otherwise with K = \int_{\Gamma : E<H<E+ΔE} d \Gamma a) Show that ΔE →0, then p(\Gamma) = \frac{\delta (E-H)}{\int_{\Gamma : H=E} \delta(E-H)} b) Show that if...

Homework Statement Consider a system consists of two subsystem A and A' in which A contains 3 spins and A' contains 2 spins. Suppose that, when the systems A and A' are initially separated from each other, measurements show the total magnetic moment of A to be - 3{\mu _0} and the total...

Can anyone help me with this, please? It's about how you go about trying to decide if two distributions are consistent, statistically speaking; specifically, what statistical test, or tests, is (are) most appropriate to use. Here's the data: N(A) N(B) G/R/P 0043 0046 #101 0264 0235...

Homework Statement Consider a random walker in one dimension, which can take right or left steps with equal probability. Assume that the walker starts at the location k>0 and there is an absorbing wall at point labelled as 0, that means if the walker reaches 0 the process stops and he stays...

I'm looking for a book on statistical physics. One's I've used already are Huangs Intro one and Sachs/Sens/Sexton. They're both great and the problems are great but neither provide answers nor are there any solutions to be found online so I have no idea if I understand the material. Could...

I have a set of data that was recorded from an engine that we are testing. We've noticed lately that a particular pressure value will sometimes spike with no apparent explanation, as seen in the attached graph. The pressure in question is passively regulated by a pump, but it is also dependent...

I have a question about statistical operator. In statistical physics you deal with temperature. So for example ##\hat{\rho}=\frac{1}{Z}e^{-\beta \hat{H}}## where ##\beta=\frac{1}{k_BT}##. In definition there is temperature. And also equivalent definition is ##\hat{\rho}=\sum_i w_i|\psi_i\rangle...

Homework Statement \frac{dq}{dT}=\sum_{i} g_i \frac{dq}{dT} e^{-\frac{ε_i}{kT}} = \frac{1}{kT^2}\sum_{i} g_i ε_i e^{-\frac{ε_i}{kT}} = \frac{1}{kT^2} \bar{ε} q Homework Equations q=\sum_{i} e^{-\frac{ε_i}{kT}} or for degenerate states, q=\sum_{I} g_i e^{-\frac{ε_I}{kT}} The Attempt at a...

Homework Statement Consider the case of a gas in the atmosphere. Assume that the temperature is a constant. Based on the Maxwell Boltzmann distribution, at sea level the atmosphere contains 78.1% N2, 21% O2, 0.9% Argon, and 0.036 CO2. What are the ratios at the the top of Everest? (Molecular...

Here are to challenge questions given to the class to answer to be turned for a free slice of pizza. We have to days, and he said we can get help, and I'm taking him at his word. Here they are. 1). Suppose a room is divided into the front fifth, the middle fifths, and the back two fifths...

Homework Statement In a large system of distinguishable harmonic oscillators, how high does the temperature have to be for the probable number of particles occupying the ground state to be less than 1? Homework Equations N(E_{n})=NAe^{\frac{-En}{K_{B}T}} E_{0}=0 (the textbook...

For the people who are in either of these fields, which math did you encounter most frequently in the field? Abstract Algebra, Analysis, Probability, Statistics, Calculus, or other? I have taken introductory courses for both topics at university and both seem to involve a wide range of math...

The derivation of the momentum/position Heisenberg Uncertainty Principle (HUP) is based on the statistical interpretation which says that if we have a lot of quantum systems in identical states, and measure the momentum in half of them and get a distribution with standard deviation σp, and...

Was Debye's basic idea for a solid body to neglect the dispersion Einstein talked about in his model?

Homework Statement Individual hydrogen atoms have been prepared in the energy state n = 2. However, nothing is known about the remaining quantum numbers. Fine structure and all corrections can be ignored. What is the micro-canonical statistical operator. Homework Equations \hat{\rho_{mc}} =...

Homework Statement Homework Equations The Attempt at a Solution To be honest I'm clueless. I've missed a large amount of the course and just struggling to find any sources that explain this. I don't want the answer to the question, I want to figure that out for myself. What I really need is...

Homework Statement Just trying to understand something my instructor said. For large n, the volume of the sphere exists in a thin shell at its surface. He asked us what relationship this has to statistical physics. Homework Equations The Attempt at a Solution The only thing I can...

Hello, i need solve de following integral \int ^{\infty}_0 \frac{x^3}{e^x+1} dx i tried with the fermi function but the factor e^x is different to e^{x-\eta}, and with the gamma function but the factor e^x+1 is different to e^x-1. Help please

So the probabilistic studying of Quantum statistics of Böse-Einstein suggests that we permutate the number of objects (objects, are the blocks (Gi-1), and the particles in the boxes Ni) and divide those by Ni! And (Gi-1)! Because these particles are identical. But the case of Fermi-Dirac, where...

Why does Quantum Mechanics have objective statistical characteristic,but does not have subjective statistical characteristic? QM has two axioms: 1-To each dynamical variable there coresponds a linear operator,and the possible values of the dynamical variable are the eigenvalues of the...

I am specifically referring to textbook "Statistical Mechanics" by Kerson Huang. It is not a general physics question, I am just trying to understand what is written in this specific book. So you can only really help if are familiar with it and have it at hand. I'm having trouble following...

I actually have no idea on how would we conduct our statistical analysis for our design project. We will be creating a digital alarm clock with an improvised sensor and we will also be conducting series of tests for it. Now our teacher is looking for the statistical analysis. Our testings are...

Homework Statement I am supposed use stat mech to find the particle density in Earth's atmosphere given only the particle mass, and temperature, and the planet's mass I guess. And I don't really know where to begin. Obviously I need to use the grand canonical ensemble but I don't know where to...

hi guys I want to know What is the mulitiplicity or statistical weight g of an energy level ? please, indetails