Quantum Mechanics

Non-relativistic theory of microscopic systems built on Hilbert spaces, operators, and probability amplitudes.


foundation tier

Quantum Mechanics is a topic within modern and quantum. Non-relativistic theory of microscopic systems built on Hilbert spaces, operators, and probability amplitudes. The area sits at the intersection of foundational theory and active research practice, and its methodology is shaped by a small set of canonical references that frame how problems are posed, how results are validated, and what counts as progress.

Work in this area progresses along several axes: the canonical theoretical framework, benchmark problems that calibrate methods against known answers, computational and experimental tooling that extends reach to larger or more complex systems, and frontier questions that current references either open up or partially answer. The references cited below illustrate these axes in different ways and together define the working vocabulary of the field.

Foundational references

The primary references for this topic establish the conceptual core and the standard problem set.

Modern Quantum Mechanics (Sakurai et al., 2017) is treated here as a primary reference for this area; its presentation of the subject is the canonical entry point for learners moving from prerequisites into independent work on quantum mechanics.

Introduction to Quantum Mechanics (Griffiths et al., 2018) is treated here as a primary reference for this area; its presentation of the subject is the canonical entry point for learners moving from prerequisites into independent work on quantum mechanics.

Open methodological questions in quantum mechanics include the precise scope of validity of the current dominant techniques, the integration of newer computational or experimental tools, and how this topic connects to neighbouring areas in the tree. Subsequent waves of editing will deepen these connections and add fresh frontier references as the literature evolves.

Prerequisites

Sources

  • textbook · primary · 2017
    Modern Quantum Mechanics
    sakurai-2017, napolitano-2017
  • textbook · primary · 2018
    Introduction to Quantum Mechanics
    griffiths-2018, schroeter-2018

In context

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Explore

  1. 01

    Wave Mechanics

    Schrödinger equation, wavefunctions, and standard problems (particle in a box, harmonic oscillator, hydrogen atom).

  2. 02

    Matrix Mechanics

    Heisenberg picture, operator algebra, and spin systems as discrete quantum models.

  3. 03

    Scattering Theory

    Cross sections, partial-wave expansion, T-matrix, and Born approximation for non-relativistic scattering.

  4. 04

    Perturbation Theory

    Time-independent and time-dependent perturbative methods for small couplings and external fields.

  5. 05

    Path Integral Formulation

    Feynman's sum-over-histories approach to quantum amplitudes.

  6. 06

    Open Quantum Systems

    Lindblad dynamics, decoherence, and master equations for system–environment coupling.

  7. 07

    Quantum Measurement

    POVMs, weak and continuous measurements, and the quantum measurement problem.

  8. 08

    Quantum Foundations

    Bell inequalities, contextuality, interpretations, and the operational structure of quantum theory.

  9. 09

    Quantum Entanglement

    Bipartite and multipartite entanglement, measures, and Bell-test phenomenology.

  10. 10

    Many-Body Quantum Mechanics

    Symmetrized states, second quantization, and effective theories for interacting quantum systems.

  11. 11

    Relativistic Quantum Mechanics

    Klein–Gordon and Dirac equations and the transition to quantum field theory.

  12. 12

    Quantum Decoherence

    Loss of quantum coherence from system–environment entanglement and its emergent classical limit.

  13. 13

    Quantum Error Models

    Noise channels, master equations, and their physical instantiations in real devices.

  14. 14

    Quantum Walks

    Discrete- and continuous-time quantum walks and their algorithmic applications.


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