# What is Quantum statistical mechanics: Definition and 17 Discussions

Quantum statistical mechanics is statistical mechanics applied to quantum mechanical systems. In quantum mechanics a statistical ensemble (probability distribution over possible quantum states) is described by a density operator S, which is a non-negative, self-adjoint, trace-class operator of trace 1 on the Hilbert space H describing the quantum system. This can be shown under various mathematical formalisms for quantum mechanics. One such formalism is provided by quantum logic.

View More On Wikipedia.org
1. ### I Determining the Number of Points in the n-Space

Electron gas is a collection of non - interacting electrons. If these electrons are confined to certain volume (for example, cube of metal), their behavior can be described by the wavefunction which is a solution to the particle in a box problem in quantum mechanics. Allowed energy states for...
2. ### Entropy of spin-1/2 Paramagnetic gas

As we know, dipole can be only arranged either parallel or anti-parallel with respect to applied magnetic field ## \vec{H} ## if we are to use quantum mechanical description, then parallel magnetic dipoles will have energy ## \mu H ## and anti-parallel magnetic dipoles have energy ## -\mu H##...
3. ### I Exceptions to the postulate of equal a priori probabilities?

Not sure if this is the appropriate forum for this, hopefully if it isn't someone can move it to a more appropriate place. The fundamental postulate of equal a priori probabilities in statistical physics asserts that all accessible microstates states in an ensemble happen with equal...
4. ### I Change of variables in the Density of States function

I have a problem where I am given the density of states for a Fermion gas in terms of momentum: ##D(p)dp##. I need to express it in terms of the energy of the energy levels, ##D(\varepsilon)d\varepsilon##, knowing that the gas is relativistic and thus ##\varepsilon=cp##. Replacing ##p## by...
5. ### A Do bosons contradict basic probability laws?

This questions was brought to my attention by Kazu Okayasu. According to probability theory the probabilities of mutually exclusive events add upp. As an example we can distribute 2 balls in two boxes with two compartments each. So there's a box on the left with a lower and an upper compartment...
6. ### Troubleshooting the Partition Function for a System with 3 Spins

I'm having problems solving the partition function. I've attached a photo of where I currently am. Am I on the right track? What should be my next step?
7. ### A How far can one change a model before it leaves the universality class

Usually, critical phenomena can be categorized in some kind of universality class which determines the critical exponent. A typical example is the class of the Ising model; adding a next-nearest-neighbour hopping term does not change the critical behavior. The typical explanation is that the...
8. ### Average speed of molecules in a Fermi gas

My first most obvious attempt was to use the relation ##<\epsilon> = \frac{3}{5}\epsilon_F## and the formula for kinetic energy, but this doesn't give the right answer and I'm frankly not sure why that's the case. My other idea was to use the Fermi statistic ##f(\epsilon)## which in this case...
9. ### Maximum value of Von Neumann Entropy

Homework Statement Prove that the maximum value of the Von Neumann entropy for a completely random ensemble is ##ln(N)## for some population ##N## Homework Equations ##S = -Tr(ρ~lnρ)## ##<A> = Tr(ρA)## The Attempt at a Solution Using Lagrange multipliers and extremizing S Let ##~S =...
10. ### B What is Quantum Statistical Mechanics?

Is Quantum Statistical Mechanics being the application of Quantum Mechanics on the separate particles of bulk matter or the application of QM on whole agregate matter?
11. ### A Normalization constant of Fermi Dirac distribution function

Fermi-Dirac distribution function is given by f(E)=(1)/(Aexp{E/k_{B}T}+1) here A is the normalization constant? How we can get A? E is the energy, k_{B} is the Boltzmann constant and T is the temperature. thank you
12. ### 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...
13. ### Reference for Axiomatic Quantum Statistical Mechanics

I have gone through two volumes of Cohen (Quantum Mechanics). Now I need a book on Quantum Statistical Mechanics. The book should use axiomatic formulation using density matrix. Please give me a suggestion. ( I'm also introduced with 2nd quantization slightly) Thanks for any help in advance.
14. ### Analytic Continutation of Quantum Statistical Mechanics

In A. Zee's book "QFT in a Nutshell" he glosses over the idea that the path integral approach and the partition function are related loosely by the correspondence principle, and alludes to some deep fundamental insight behind QFT. But then he moves on. Anyone know where I could read up more on this?
15. ### Quantum Statistical Mechanics

Having learned the fundamentals of quantum mechanics from Ballentine, I am now looking around for books on quantum statistical mechanics. However, I find most of them in-complete. I don't want to fuss, but I really liked Ballentine's approach and would like to continue with something similar. Do...
16. ### Quantum Statistical Mechanics

Hi there PF. I just want to ask, whether Quantum Statistical Mechanics is a Quantum field theory. If not, is there anything else that describes entropy and thermodynamics in terms of a Quantum field theory?
17. ### Question about quantum statistical mechanics and thermodynamic arrow of time

I got into a discussion about the "arrow of time" recently, and one point I brought up is that for a system governed by time-symmetric laws, if you place no special restrictions on the initial conditions but instead pick an initial state randomly from the system's entire phase space, you will be...