Quantum statistical mechanics

Modern physics
${\displaystyle {\hat {H}}|\psi _{n}(t)\rangle =i\hbar {\frac {d}{dt}}|\psi _{n}(t)\rangle }$ ${\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }={\kappa }T_{\mu \nu }}$ Schrödinger and Einstein field equations
Founders Max Planck Albert Einstein Niels Bohr Max Born Werner Heisenberg Erwin Schrödinger Pascual Jordan Wolfgang Pauli Paul Dirac Ernest Rutherford Louis de Broglie Satyendra Nath Bose
Concepts Topology Space Time Energy Matter Work Randomness Information Entropy Light Particle Wave
Branches Applied Experimental Theoretical Mathematical Philosophy of physics Quantum mechanics Quantum field theory Quantum information Quantum computation Electromagnetism Weak interaction Electroweak interaction Strong interaction Atomic Particle Nuclear Atomic, molecular, and optical Condensed matter Statistical Complex systems Non-linear dynamics Biophysics Neurophysics Plasma physics Special relativity General relativity Astrophysics Cosmology Theories of gravitation Quantum gravity Theory of everything
Scientists Witten Röntgen Becquerel Lorentz Planck Curie Wien Skłodowska-Curie Sommerfeld Rutherford Soddy Onnes Einstein Wilczek Born Weyl Bohr Kramers Schrödinger de Broglie Laue Bose Compton Pauli Walton Fermi van der Waals Heisenberg Dyson Zeeman Moseley Hilbert Gödel Jordan Dirac Wigner Hawking P. W. Anderson Lemaître Thomson Poincaré Wheeler Penrose Millikan Nambu von Neumann Higgs Hahn Feynman Yang Lee Lenard Salam 't Hooft Veltman Bell Gell-Mann J. J. Thomson Raman Bragg Bardeen Shockley Chadwick Lawrence Zeilinger Goudsmit Uhlenbeck
Categories Modern physics
v t e

Part of a series of articles about
Quantum mechanics
${\displaystyle i\hbar {\frac {d}{dt}}|\Psi \rangle ={\hat {H}}|\Psi \rangle }$ Schrödinger equation
Introduction Glossary History
Background Classical mechanics Old quantum theory Bra–ket notation Hamiltonian Interference
Fundamentals Complementarity Decoherence Entanglement Energy level Measurement Nonlocality Quantum number State Superposition Symmetry Tunnelling Uncertainty Wave function Collapse
Experiments Bell's inequality Davisson–Germer Double-slit Elitzur–Vaidman Franck–Hertz Leggett–Garg inequality Mach–Zehnder Popper Quantum eraser Delayed-choice Schrödinger's cat Stern–Gerlach Wheeler's delayed-choice
Formulations Overview Heisenberg Interaction Matrix Phase-space Schrödinger Sum-over-histories (path integral)
Equations Dirac Klein–Gordon Pauli Rydberg Schrödinger
Interpretations Bayesian Consistent histories Copenhagen de Broglie–Bohm Ensemble Hidden-variable Local Superdeterminism Many-worlds Objective collapse Quantum logic Relational Transactional Von Neumann–Wigner
Advanced topics Relativistic quantum mechanics Quantum field theory Quantum information science Quantum computing Quantum chaos EPR paradox Density matrix Scattering theory Quantum statistical mechanics Quantum machine learning
Scientists Aharonov Bell Bethe Blackett Bloch Bohm Bohr Born Bose de Broglie Compton Dirac Davisson Debye Ehrenfest Einstein Everett Fock Fermi Feynman Glauber Gutzwiller Heisenberg Hilbert Jordan Kramers Lamb Landau Laue Moseley Millikan Onnes Pauli Planck Rabi Raman Rydberg Schrödinger Simmons Sommerfeld von Neumann Weyl Wien Wigner Zeeman Zeilinger
v t e

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.