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Modern Physics: Quantum Mechanics

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The core ideas of quantum mechanics.

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Quantum mechanics

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  1. 1Quantum mechanics
    The fundamental physical theory that describes the behavior of matter and light at and below the scale of atoms
  2. 2What does quantum mechanics serve as the foundation for?
    Quantum chemistry, quantum biology, quantum field theory, quantum technology, and quantum information science
  3. 3Wave-particle duality
    The phenomenon where quantum systems show characteristics of both particles and waves
  4. 4Uncertainty principle
    The principle stating there are limits to how accurately the value of a physical quantity can be predicted prior to measurement
  5. 5Wave function
    A mathematical entity that provides information, in the form of probability amplitudes, about what measurements of a particle's properties may yield
  6. 6Born rule
    The rule stating that probability is found by taking the square of the absolute value of a complex number (probability amplitude)
  7. 7What does the Schrödinger equation describe?
    The time evolution of a quantum state, relating probability amplitudes at one moment to those at another
  8. 8Most famous form of the uncertainty principle
    It's impossible to have simultaneous precise predictions for measurements of both position and momentum
  9. 9What does the double-slit experiment demonstrate?
    Quantum interference, showing that particles exhibit wave-like behavior producing interference patterns
  10. 10What happens in the double-slit experiment when detectors are placed at the slits?
    The interference pattern disappears; each photon passes through one slit (not both) and behaves classically
  11. 11Quantum tunneling
    A phenomenon where a particle can cross a potential barrier even if its kinetic energy is smaller than the barrier's maximum
  12. 12What important technologies rely on quantum tunneling?
    Scanning tunneling microscopy, tunnel diodes, tunnel field-effect transistors, and enabling radioactive decay and nuclear fusion
  13. 13Quantum entanglement
    When quantum systems interact and their properties become so intertwined that they cannot be described independently
  14. 14What did Schrödinger call entanglement?
    The characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought
  15. 15Can entanglement be used to send signals faster than light?
    No, as demonstrated by the no-communication theorem
  16. 16Bell's theorem
    A theorem showing that if nature operates according to local hidden variables, then Bell test results will be constrained in a specific way
  17. 17What have Bell tests shown?
    Results incompatible with the constraints imposed by local hidden variables, supporting quantum mechanics
  18. 18State of a quantum mechanical system mathematically
    A vector belonging to a separable complex Hilbert space
  19. 19Observables in quantum mechanics
    Hermitian (self-adjoint) linear operators acting on the Hilbert space, representing physical quantities like position, momentum, energy, and spin
  20. 20Eigenstate
    A quantum state that is an eigenvector of an observable, with the eigenvalue corresponding to the value of the observable in that state
  21. 21Quantum superposition
    When a quantum state is a linear combination of eigenstates
  22. 22What happens when a quantum measurement is made?
    The result will be one of the eigenvalues with probability given by the Born rule, and the state collapses to the corresponding eigenstate
  23. 23Schrödinger equation for time evolution
    iℏ(∂|ψ⟩/∂t) = Ĥ|ψ⟩, where Ĥ is the Hamiltonian operator
  24. 24Hamiltonian in quantum mechanics
    The observable corresponding to the total energy of the system
  25. 25Reduced Planck constant ℏ
    A fundamental constant (h/2π) that relates energy to frequency in quantum systems
  26. 26Is time evolution in quantum mechanics deterministic?
    Yes, given an initial quantum state, the Schrödinger equation makes a definite prediction of the state at any later time
  27. 27Stationary states
    Wave functions (eigenstates of the Hamiltonian) that produce probability distributions independent of time
  28. 28What simple quantum systems have analytic solutions?
    Quantum harmonic oscillator, particle in a box, dihydrogen cation, and hydrogen atom
  29. 29Can the helium atom be solved analytically?
    No, despite having only two electrons, it has defied all attempts at a fully analytic treatment
  30. 30Perturbation theory
    A method using analytic results for simple models to approximate solutions for related but more complicated models

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