Partition Definition and 307 Threads

Hello everybody, I registered here hoping to finally find a fundated answer about what I by myself seem not be able to figure out. Question in short: We have calculated a list of wavenumbers for some molecular systems. How do you get the vibrational partition function from that? My...

Homework Statement If you have a three energy level system, with energies 0, A, B where B>A, which consists of only two particles what is the probability that 1 of the particles is in the ground state? What about if two of them are in the ground state? Do this using both fermi and boson...

I am attempting to mesh this part using "hex" elements but I always receive an error. Am I supposed to partition the part? If so how do I do that? Thanks for you help P.S. I attached related documents to this post

Homework Statement We had to prove that an integral didn't exist by computing upper and lower sums. It was for f(x)=x for rational 0 for irrational Homework Equations The Attempt at a Solution Lower was easy, it's just 0 (inf of any interval is 0). But the upper...

I've a set of N numbers with n size, and I want to find to each partition they belong. E.g., a set with numbers from 1 to 210, with 3 partitions. So, the numbers from 1 to 70 goes to partition 1, from 71 to 140 goes to partition 2, and from 141 to 210 goes to partition 3. How can I calculate...

Hey, If I have a canonical partition function with: Z=\frac{1}{h}Z_{Pot}\cdot Z_{Kin}. Can i callculate immediately the average potential Energy, by: \bar{U}=-\frac{\partial}{\partial \beta}\ln(Z_{pot}) ?

Two ideal gases are separated by a partition which does not allow molecules to pass from one volume to the other. Gas 1 has: N1, V1, T1, Cv1 for the number of molecules, volume it occupies, temperature in kelvin, and specific heat per molecule at constant volume respectively. Gas 2 has: N2, V2...

I'm studying phase transitions in statistical mechanics, and I'm curious to know more about how the partition function becomes zero. I've read a bit about the Lee Yang theorem, but haven't found a good description of the whole program. Does anyone have a good paper on the subject? (Other than...

Homework Statement Consider a system of N distinguishable, non-interacting harmonic oscillators. The Hamiltonian is given (shown below). Assuming that the oscillators obey Schrodinger's equation, determine the canonical partition function for the system. Then assume the oscillators obey...

Hi everyone, I'm reading some lecture notes on statistical physics and thermodynamics and I'm stuck at an expression for a partition function which I really don't understand. The chapter is on mean field theory and the discussion is about hard spheres on a lattice. The interaction of the hard...

Why in case of Ising model ##H=-J\sum S_iS_{i+1}## we calculate canonical partition function?

Hi, I have a question about the partition function. It is defined as ## Z = \sum_{i} e^{-\beta \epsilon_{i}} ## where ##\epsilon_i## denotes the amount of energy transferred from the large system to the small system. By using the formula for the Shannon-entropy ##S = - k \sum_i P_i \log...

Homework Statement Show that the partition function for a composite system, let's call it '3', composed of systems '1' and '2' is the product of the partition functions of '1' and '2' independently.Homework Equations Kittel defines partition functions using the fundamental temperature τ (which...

Homework Statement Consider a two dimensional surface on a three dimensional crystal. This surface has M positions that can adsorb particles, each of which can bind one particle only and an adsorption does not affect the adsorption on nearby sites. An adsorbed particle has energy ε and an...

Hi there, I am reading an article, but I faced the following problem, and I am wondering if it is well known fact. If the integral of a function on some interval is infinity, can we partition this interval into countable disjoint (in their interiors) subintervals such that the integral...

I'm not sure if this is the right place to ask.. Anyway. Assume we have some integral I with 0 and 2 as limits. I = 3∫xexdx from 0 to 2. What exactly do we have to do to find the partition points (and what are they?) but using the composite trapezoidal rule? I = 25.1671683 upon computing...

Homework Statement Imagine a system with N distinguishable particles. Each particle may be in two states of energy: -ε and +ε. Find the the partition function of the system Homework Equations The Attempt at a Solution I know that I have to find the partition function for a...

Homework Statement Are the following subsets partitions of the set of integers? The set of integers divisible by 4, the set of integers equivalent to 1 mod 4, 2 mod 4, and 3 mod 4. Homework Equations The Attempt at a Solution Yes, it is a partition of the set of integers...

Is there a physical process in thermodynamics that results the value of the partition function as zero? When partition function is zero, then free energy becomes infinity, and it also yields negative entropy (at least within the system). Are there physical meanings of these?

I have a moderately sized music collection of 76GB which I would like to access from both ubuntu and windows. What is the best way to do this? My thoughts were... have ubuntu on one partition, windows on a second, and stick shared stuff in a third one. Is there software for both ubuntu and...

is it true that as the lipid water partition coefficient increases, the permeability of lipid increases and the permeability of water lowers. does that mean that a substance w/ a high lipid water partition coeffecient will be able to go through the cell membrane more easily and cause hemolysis...

\int^{b}_{a}f(x)dx = \int^{c}_{a}f(x)dx + \int^{b}_{c}f(x)dx If one of the integrals on the right-hand-side is known to diverge, must the integral on the left also necessarily diverge? BiP

Hello guys, I work on a final project study discussed the use of optimization methods. The project in question consists in partitioning a grid dimensions NXM grids in dimensions 3 X 3 (which share no box) to the extent possible, otherwise find grids of dimensions 3 x 3 which are dependent...

sorry if i posted this topic here..let P1 and P2 be a path partition of a graph.is it possible that P1 and P2 to have the same end vertices?

I've derived Z for the quantum harmonic oscillator and was wondering if anyone could verify I did everything correctly. I don't have any experience working with exponential traces so I want to make sure I'm using them correctly. Z is defined as \mathcal{Z}= tr(e^{-\beta H}). So the natural...

The grand partition function Z of a system is given by formula: Z = Ʃ exp ((-Ei/KbT) + (μni/KbT)) where , 1, 2... i E i= are permitted energy levels, μ is the chemical potential, , 1,2... i n i= are number of particles of different types. Taking into account that averaged internal...

I've been working on this Linear Algebra problem for a while: Let F be a field, V a vector space over F with basis \mathcal{B}=\{b_i\mid i\in I\}. Let S be a subspace of V, and let \{B_1, \dotsc, B_k\} be a partition of \mathcal{B}. Suppose that S\cap \langle B_i\rangle\neq \{0\} for all i...

Homework Statement By what factor does the total partition function (excluding electronic) increase when 20 m^3 of Neon at 1.00 atm and 300 K is allowed to expand by 0.0010%? Homework Equations translational partition function qt= (V×[(2∏mkT)]^3/2])/ (h^3), vibrational partitition...

Homework Statement For a system A consists of two parts A' and A'' which interact only weakly with each other, if the states of A' and A'' are labeled respectively by r and s, then a state of A can be specified by the pair of numbers r,s and its corresponding energy E_{rs} is simply...

Homework Statement An impurity can be occupied by 0, 1 or 2 electrons. The impurity orbital in non-degenerate, except for the choice of electron spin. The energy of the impurity level is \epsilon, but to place the second electron on the site requires an additional energy \delta \epsilon...

The probability of finding the system in microscopic state i is: p_{i}=\dfrac{1}{Q}e^{-\beta E_{i}} Where Q is the partition function. Assumption: molecule n occupies the i_{n}th molecular state (every molecule is a system). The total energy becomes...

Q: Suppose that the oscillation ω_f (x) of a function f is smaller than η at each point x of an interval [c,d]. Show that there must be a partition π of [c,d] s.t. the oscillation ωf([x_(k-1),x_k ])<η on each member of the partition. My solution (Rough sketch): This condition on x is...

If I have a totally ordered set and then create a noncrossing partition of that set it seems intuitively obvious that each block of the partition would be totally ordered as well. Can I assume this inheritance or do I need to prove each block is totally ordered? How would one go about proving...

Homework Statement I would like to calculate the grand canonical partition function (GCPF) for a system in which there are are m lattice sites. A configuration may be specified by the numbers (n_1, n_2, ... , n_m), where n_k = 1 if a particle occupies site k and n_k = 0 if no particle occupies...

For the given set A, determine whether P is a partition of A. A= ℝ, P=(-∞,-1)\cup[-1,1]\cup(1,∞) Is it correct to say that P is not partition? I don't understand why. Thank you

For the given set A, determine whether P is a partition of A. A= {1,2,3,4,5,6,7}, P={{1,3},{5,6},{2,4},{7}} Is it correct to say that P is a partition of A? Thank you

For the given set A, determine whether P is a partition of A. A= {1,2,3,4}, P={{1,2},{2,3},{3,4}} Is it correct to say that P is a partition of A? Thank you

Homework Statement A atom had a threefold degenerate ground level, a non degenerate electronically excited level at 3500 cm^-1(setting the energy orgin as the ground electronic state energy of the atom ) and a threefold degenerate level at 4700 cm^-1 . Calculate the electronic partition...

Homework Statement We have a single particle that can be in one of three different microstates, \epsilon_0, \epsilon_1 or \epsilon_2, with \epsilon_0 < \epsilon_1 < \epsilon_2. The particle is in thermal equilibrium with a heat bath at temperature T. 1) Calculate the canonical partition...

I have some confusions identifying the following objects: (1)Some transition amplitude involving time evolution(Peskin page 281, eqn 9.14): \langle\phi_b(\mathbf x)|e^{-iHT}|\phi_a(\mathbf x)\rangle=\int{\cal D\phi \;exp[i\int d^4x\cal L]} (2)Partition function(after wick rotation)...

Homework Statement Assume that it is appropriate to transfer the probabilities IP(F|L) and IP(F|T) from the police context to the insurance context. Define the following new events for the insurance context: L = “insurance claimant is lying”; T = “insurance claimant is truthful”; F =...

While reading an article about superconductivity I found out a strange partition function which I don't know how to re-obtain. The partition function is given by: Z=-\prod_{\omega,\mathbf{k}} (\omega^2 + E(\mathbf{k})^2) where the sum over \omega runs over Matsubara frequencies and...

hi folks, I want to calculate the potential energy part of the partition function of 2 particles interacting via the Lennard-Jones potential. This partition function should be proportional to: \int_0^\infty exp(-\beta * 4((\frac{1}{r})^{12}-(\frac{1}{r})^6)) dr But this integral won't...

[b]1. A pendulum of mass m hangs from a weightless string of length l The string makes an angle θ with the vertical Find (i) <θ> (ii) <θ^2> (iii) <v> (iiii) <v^2> Homework Equations The Hamiltonian in terms of θ and the angular momentum L= H= L^2/2ml^2 + mgl(1-cosθ) The...

I need some help with this problem: Consider a diatomic molecule closed in a cubic container of volume V which hamiltonian is: H=\frac{p_1^2}{2m}+\frac{p_2^2}{2m}+\frac{K}{2}| \vec r_2 - \vec r_1|^2 where \vec r_1, \vec r_2 are the positions of the two atoms. a) Find the partition function...

Homework Statement What exactly does partition coefficient tell us? if I have a low partition coefficient, does that mean its less soluble in that compound? Homework Equations The Attempt at a Solution I had .0555g Benzoic acid mixed with water and methylene chloride. It...

Well what is the partition function of harmonic oscillator with this energy E=hw(n+1/2) , n=1,3,5,... Z=e^(-BE) right? B=1/KT^2 How to expand this? Thank you.

Find the number of the partition of the alphabet {A,b.....Z} of the type (2,2,2,3,3,3,3,4,4) So I did 26!/(2!2!2!3!3!3!3!4!4!) = A REALLY BIG NUMBER then I took that number and dived it by (3!4!2!) and got 2.344 x10^17 which seems to big to be an answer. So I'm wondering if the number...

Homework Statement 1. If the system, which has N identical particles, only has two possible energy states E=0,e(e is an energy) ,what's the ensemble average of E? 2. Find the partition function which has two identical Fermion system if the energy states only have E=0,e.Homework Equations I...

In my statistical physics class the partition function Z is used in the calculation of probabilities, and I even have a formula for it: Z=\sume-E/kT. While this is all very good I am having some trouble actually grasping what it is, qualitatively speaking. Would someone please be able to...