Partition Definition and 265 Threads

I have a really conceptual question on vibrational partition function for a diatomic molecule.If we consider a diatomic molecule, we write : Energy of simple harmonic oscillator=E_{i}=(n + 1/2) h\nu.We plug this eqn. into Z_{vib}=\sum e^{-\beta\epsilon_{i}}. Now , my question, is that the...

Hello. I come across a problem: how to calculate the partition function of a classical spring whose energy is 1/2kx^2, and use thermodynamics to show that the force on the spring is linearly proportional to its elongation x? I got stuck at the first step. What is the energy of the spring, is...

Basic question: meaning of "partition of R into maximal connected intervals" What does the phrase "partition of R into maximal connected intervals" mean? The full sentence: "Let I_1, I_2, ... ,I_m be the partition of R into maximal connected intervals with disjoint interiors."

Homework Statement I. Finding the partition function Z. II. If the middle level (only) is degenerate, i.e. there are two states with the same energy, show that the partition function is: Z = (1+exp(\frac{-\epsilon}{k_{B}T}))^{2} III. State the Helmholtz free energy F of the...

In looking at phonons, and their energy, I came across the Partition function. THis was needed to calculate the internal energy of the solid. But howcome the Partition function is used, and not the GRAND Partition function? The number of phonons is not conserved, I know that, but isn't N, the...

I recently installed ubuntu netbook remix on my newly bought netbook to try it out. I created a new partition on my HDD from the free disk space to install ubuntu on. So right now I have dual boot ubuntu and windows xp. The ubuntu netbook remix turned out to be more buggy than I thought and I'm...

Hello everyone, I have passed my integral calculus class and it's been a little while so I don't really remember everything. Can anyone help me out with this? Homework Statement Let f(x) = sqrt(x), x E [0,1] and P=\left \{ 0,\left ( \frac{1}{n} \right )^{2}, \left ( \frac{2}{n} \right...

Homework Statement This is just a general question, not a "problem" Homework Equations Z = sum(e^Ej/kT) The Attempt at a Solution I'm working on a problem in which I'm asked to find the probabilities of an electron in a hydrogen atom being at one of three energies. The...

Hi, I've been trying to find out the ways in which an odd integral number can be represented by smaller integers such that the even integers occur an even number of times. So for example, the number 15 has the following representations: 15: 2+2+2+2+2+2+3 (even integer 2 occurs even number...

Homework Statement For n>14 such that n is an integer, prove that a square can be partitioned into n smaller squares... Homework Equations None... The Attempt at a Solution I was thinking this would be somewhat of an induction proof because we are working our way up to n. So far...

Question is on attachment file.

I am reading a book (Di Francesco's "CFT", pg 337) in which it is given that if we take the operator that translates the system along some direction (which is a combination of time and space) as 'A', then the partition function is just trace(A). How do we get this?

Homework Statement Calculate fermi energy, fermi temp and fermi wave vector. a)Protons with n= 1.0E43 m^{-3} b) ^{3}He in liquid He (atomic volume= 46E^-3 m^3 Homework Equations E_f=\frac{h^2}{8 m} (\frac{3 n}{\pi V})^\frac{2}{3} T_f= \frac{E_f}{k_B} The Attempt at a Solution I get the...

Homework Statement By shining and intense laser beam on to a semiconductor, one can create a collection of electrons (charge -e, and effective mass me) and holes (charge +e, and effective mass mh) in the bulk. The oppositely charged particle may pair up (as in a hydrogen atom) to form a gas of...

Does there exist a database for the Partition function at different temperatures? As I understand it it only varies with temperature and is otherwise the same for the species. I am looking for the partition function for C02 at T=1000K.

Hi All - If I have a potential energy surface with two energy states, one higher than the other, where I can make the assumption that both potential wells can be approximated via harmonic potentials with force constants kA and kB then would the partition function for the system be...

Homework Statement Partition the following collection of groups into subcollections of isomorphic groups. a * superscript means all nonzero elements of the set. integers under addition S_{2} S_{6} integer_{6} integer_{2} real^{*} under multiplication real^{+} under multiplication...

write a function called int partition(int arr[], int size) which input an array of integers and decides whether it is possible to divide the array into two groups so the sums of both the groups will be equal. for example arr = {1,2,2,3,5,6,1} its could be divided into {2,2,6} and...

Homework Statement This is the integration i have to solve I=\int x^{2}In(1-exp(-ax))dx integration is from zero to infinity The Attempt at a Solution I know that it should be solved with integration by parts so u=In(1-exp(-ax)) du=[a exp(-ax)] / [1-exp(-ax)] dv=x^{2}dx...

Hello! I've got a problem. If you scroll down to page 118 on the following link http://books.google.com/books?id=ntrPDA6zE1wC&dq=Quarks+bound+by+chiral+fields&pg=PP1&ots=_29vGOurGs&source=bn&sig=h4vGPNBbKX14DpoOyt4tuRZHkRc&hl=de&sa=X&oi=book_result&resnum=4&ct=result#PPA118,M1 there you...

I am aware that there are several generator functions for the Partition Function p(n), but does anyone know if a closed form formula exists for this function?

Homework Statement Prove that the nonempty fibers of a map form a partition of the domain. The Attempt at a Solution Ok so we have some map phi: S -->T And we want to show that its pre-image phi-1(t) = {s in S | phi(s)=t} forms a partition of the domain. Im really confused here. I assume...

Homework Statement For a magnetic particle with an angular momentum "quantum number", j, the allowed values of the z component of a particles magnetic moment are: µ = -jδ, (-j + 1)δ, ..., (j-1)δ, jδ δ is a constant, and j is a multiple of 1/2 Show that the partition function of a...

For the set A = {1,2,3,4,5,6,7}, determine whether script A is a partition of A. script A = {{1,3,},{5,6}, {2,4},{7}} Describe the partition for the equivalence relation T defined for x,y \in \mathbbc{R} by X T y iff \left[ \left[x \right] \right] = \left[ \left[y \right] \right] where...

The question: A system consists of N sites and N particles with magnetic moment m. each site can be in one of the three situations: 1. empty with energy zero. 2. occupied with one particle and zero energy (when there isn't magnetic field around). 3. occupied with two particles with anti...

given a partition function of the form Z[u]= \prod Z_{i} [u] Z_{i} [u] = \sum_{n=-\infty}^{\infty}e^{iuE_{n}^{i}} what is the meaning of zeros ? i mean the values that make Z[u]=0 and how could we calculate these zeros ??

Homework Statement Does anyone know the mathematical definition of the microcanonical partition function? I've seen \Omega = {E_0\over{N!h^{3n}}}\int d^{3N}q d^{3N}p \delta(H - E) where H=H(p,q) is the Hamiltonian. This looks like a useful definition. Only thing is I don't know what E_0...

Homework Statement If we have a system of N independent particles and the partition function for one particle is Z_1, then is the partition function for the N particle system Z=(Z_1)^N? Homework Equations The Attempt at a Solution I'm pretty sure that this is true for a classical...

Homework Statement Suppose that we partition R^3 into horizontal planes. What equivalence relation is associated with this partition? Suppose that we partition R^3 into concentric spheres, centered at (0,0,0). What equivalence relation is associated with this partition? Homework Equations...

Homework Statement a. Let A={1,2,...10}. Describe a partition of A that gives rise to five distinct paritioning sets. b.Describe a partition of Z that gives rise to five distinct partitioning sets c. Describe a partition of R that gives rise to five distint partitioning sets Homework...

Homework Statement Describe the partition associated with the following: On Z, we define x~y if and only if x-y is divisible by 3 Homework Equations The Attempt at a Solution Could someone please give me a hint? I don't understand what I'm supposed to do. Thank you

Homework Statement A certain magnetic system has N independent molecules per unit volume, each of which as 4 distinct energy levels: 0, \Delta - \mu_BB, \Delta, \Delta + \mu_BB. i) Write down the partition function, and hence find an expression for the Hemholtz function ii) Use this...

given a partition function Tr[e^{-BH}] or Z(B)= \int_{P}dx dp e^{-BH(p,q)} is there any meaning for its zeros ? , i mean what happens in case the partition function Z(B)=0 for some 'B' or temperature B=1/kT do these zeros have a meaning ?? thanks

In an Excel group someone connected with the Texas caucus gave this math problem> how to subdivide the following set of precincts into subsets so that there are a maximum number of subsets from this set with each subset of precincts totaling at least 180 votes. Since the caucus is this month it...

Homework Statement Use a graphing utility to approximate the partition numbers of the function f(x) to two decimal places. Then solve the following inequalities. (a) f(x)>0 (b) f(x)<0 Express all answers in interval notation Homework Equations The Attempt at a Solution...

Is it possible to obtain the relation S = \log Z + \langle U \rangle /T directly from the Boltzmann distribution? Edit: It seems that we can if we use the VN entropy: S = -\Sigma p_i \log p_i This suggests that the entropy of a single microstate should be s = -\log( \frac{e^{-\epsilon...

Partition function for a gas in a cylinder -- urgent! Hi, Here's the problem -- it's supposed to be a specimen of what I can expect in my exam, but it isn't much like the tutorial questions I've been doing. I'd really appreciate some help -- fast! Homework Statement An ideal gas consisting...

Is the energy given by the first or the second? I have seen both relationships in different websites, and I am confused. E = kT^2 \frac{\partial Z}{\partial T} or E = - \frac{\partial ln Z}{\partial \beta}

The partition function in the classical theory is an integral over phase space. Thus, the partition function is often not dimensionless. Then the formula F = -T \log Z can no longer be valid, as you can only take the logarithm of a dimensionless number. In the quantum theory, this...

What is the relation between the partition function and the Boltzman, Maxwell distribution? Differences and similarities? Both have exponentials to the power of the negative total energy of the microstate. Although the word microstate dosen't occur in the Boltzman, Maxwell case. Is the BM...

Homework Statement When modeling ideal gas molecules using a grand partition ensemble, is heat flow = 0? So if U=Q-W then in a grand canonical ensemble, U=-W?The Attempt at a Solution I think so as the system is in thermal equilibrium with the surroundings. So in this system the total energy is...

Is ther any form by bisection or simiar to obtain a partition for an infinite-dimensional interval (aka functional space)?? i believe you could obtain a partition for every interval 'centered' at a certain function as: X(t), X(t)+\delta (t-t`), X(t)+2\delta (t-t`), X(t)+\delta (t-t`), ...

So I've set up my computer to dual boot into WinXP or Fedora Core 6. As recommended by some walkthroughs I found, I've created a FAT32 partition for passing data back and forth between WinXP and linux. Alas, it only has 8 character filename support. I would like to have a partition for...

Let us consider a collection of non-interacting hydrogen atoms at a certain temperature T. The energy levels of the hydrogen atom and their degeneracy are: En = -R/n² gn = n² The partition function in statistical physics is given by: Z = Sum(gn Exp(-En/kT), n=1 to Inf) This...

If I have a 2 state system with energy levels of the 2 states to be 0 and V. I find the partition function to be Z = 1 + e^(-V/kT). Am I correct? If so, does that not mean the average energy is V? and thus the entropy is 0? This doesn't make sense, how is the entropy of a 2 state system (when 1...

Hi, I just made some changes to my partition table in linux using fdisk that are very bad. For the moment everything is fine but when I reboot those changes will take effect. Is there any way to restore my partition table from the good version that the kernel is still using? Thanks

I want to partition a number n into k parts for example 9 into 3 parts x+y+z=9 and each element must be non zero , first look tells me it's combination with repetition. however C(n-1,n-k) doesn't give the same number of possibilities when trying all of them. x+y+z=9 C(8,6)=28 while trying...

Let be the continuous partition function: Z(\beta)=(N!)^{-1}\int_{V}dx_1 dx_2 dx_3 dx_4 ...dx_N exp(-\beta H(x_1, x_2 , x_3 , ... ,x_n,p_1 , p_2 , ..., p_N if the Hamiltonian is 'quadratic' in p's are q's do this mean that the particles in the gas solid or whatever follow a Normal...

bah nevermind the question is too complicated to even write down :cry: i hate this :(

hay everyone can u help me. how u delete or format ntfs partition? i need to get it out or format it if u want to Email me it is codename951@yahoo.com thank bye :cry: