Quantum statistics Definition and 16 Threads

Particle statistics is a particular description of multiple particles in statistical mechanics. A key prerequisite concept is that of a statistical ensemble (an idealization comprising the state space of possible states of a system, each labeled with a probability) that emphasizes properties of a large system as a whole at the expense of knowledge about parameters of separate particles. When an ensemble describes a system of particles with similar properties, their number is called the particle number and usually denoted by N.

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  1. B

    A Mixed quantum state of the Bose-Einstein distribution

    Why is the quantum state of the Bose-Einstein distribution mixed and not pure? Is there any mathematical proof on this?
  2. T

    A Anti-commutation relation for quantized fields

    Could somebody elaborate following statement from wikipedia in detail on interplay between the "choice" of anti- or commutation relation for quantized fields and the the associated statistics which the field satisfies before get quantized: Very roughly the story with second quantization is one...
  3. Philip Koeck

    A Is there an Expression for Entropy of Fermions or Bosons?

    Is there an expression similar to the Sackur-Tetrode equation that describes the statistical entropy of fermions or bosons, maybe for the electron gas in a metal or the photon gas in a cavity?
  4. D

    I In quantum statistics, inhibition/enhancement factors

    These ideas come from the book Quantum Physics by Eisberg and Resnick (specifically ch11), can anyone explain what the inhibition factor and enhancement factors are in a little more detail? I do not understand what the book is trying to explain, and I can't seem to find these anywhere online...
  5. A

    I Degeneracy in quantum statistics

    degeneracy,this word appears in my textbook many times,but i could not understand what it means in quantum statistics.also in my textbook it is said in bose-einstein statistics that " the deviation from perfect gas behaviour exhibited by bose-einstein gas is called gas degeneracy".but i can't...
  6. erbilsilik

    What are the expansions of Bose functions for studying thermodynamic behavior?

    Homework Statement To study the thermodynamic behavior of the limit $$z\rightarrow1$$ it is useful to get the expansions of $$g_{0}\left( z\right),g_{1}\left( z\right),g_{2}\left( z\right)$$ $$\alpha =-\ln z$$ which is small positive number. From, BE integral, $$g_{1}\left( \alpha \right)...
  7. erbilsilik

    A Fugacity of Ideal Bose Gas: Exploring the Connection to Chemical Potential

    We know that the average occupation number cannot be negative for all systems and chemical potential must be negative in Ideal Bose Gas. This fact leads us to arrive a conclusion for fugacity which is related by chemical potential, as I quoted below: The restriction of the fugacity to the...
  8. S

    Microcanonical ensemble density matrix

    Ref: R.K Pathria Statistical mechanics (third edition sec 5.2A) First it is argued that the density matrix for microcanonical will be diagonal with all diagonal elements equal in the energy representation. Then it is said that this general form should remain the same in all representations. i.e...
  9. I

    Mathematical Quantum Statistics: Why is A*rho of trace class?

    Hi, as we know a density operator \rho is defined to be a non-negative definite operator of trace class (with trace 1). We also know that for a given observable A, which is a (possibly unbounded) self-adjoint operator, the expectation value can be calculated as \operatorname{tr}(A \cdot...
  10. S

    Quantum statistics: density of states problem

    When you consider a electron L×L×L box, I think I understand how to derive the DOS-spectrum. Unfortunately, when a small change is made to the problem, I really don't understand what to do, so I probably don't understand the theory at all.. This is the question: Homework Statement Consider a...
  11. B

    Quantum statistics expectation value

    1. What is the expectation value, <x>, for the given distribution over the interval from – to + infinity of the function: f(x)=e^(-.5(x-mu)^2(sigma^-2)) 2. This is a statistics problem i think. I just need to know how this type of problem is worked out because it is relevant to my...
  12. P

    How Can Degenerate Fermi Gases Illuminate Astrophysics and Quantum Computing?

    I'm a senior undergrad student and I am going to give a 50 minute lecture on Degenerate Fermi Gases to the Thermodynamics and Statistical Mechanics class. I was wondering if anybody could help me out with coming up with some interesting stories, factoids, thought experiments, history lessons...
  13. P

    How Can Degenerate Fermi Gases Illuminate Quantum Statistics?

    I'm a senior undergrad student and I am going to give a 50 minute lecture on Degenerate Fermi Gases to the Thermodynamics and Statistical Mechanics class. I was wondering if anybody could help me out with coming up with some interesting stories, factoids, thought experiments, history lessons...
  14. A

    Classical and Quantum Statistics

    Homework Statement Consider an atom with a magnetic moment \mu and a total spin of ½. The atom is placed in a uniform magnetic field B at temperature T. (a) Assuming Maxwell-Boltzmann statistics are valid at this temperature, find the ratio of atoms with spins aligned with the field to those...
  15. N

    Do Free Electrons Have Momentum Zero at Absolute Zero?

    [SOLVED] Quantum Statistics question Homework Statement Electrons in a metal are considered as free electron gas where (a) Fermi energy is (h^2/2m)[3N/8*pi*V]^(2/3) (b)Average energy of the free electrons at absolute zero is E(0)=(3/5)E_f where E_f is the Fermi energy (c)Pauli...
  16. G

    Between classical or quantum statistics

    Hi can someone please help me! Can someone explain when it is acceptable to quantum statistics instead of classical statistics? And what is the difference between them. Thanks All OLY
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