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  1. Wave functions of the electron in a hydrogen atom at different energy levels. Quantum mechanics cannot predict the exact location of a particle in space, only the probability of finding it at different locations. [1] The brighter areas represent a higher probability of finding the electron.

  2. In quantum physics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common symbols for a wave function are the Greek letters ψ and Ψ (lower-case and capital psi, respectively). Wave functions are complex-valued.

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    • History
    • Classical Waves and Particles
    • Electrons Behaving as Waves and Particles
    • Observing Photons as Particles
    • Duality with Other Properties
    • Which Slit Experiments
    • See Also
    • External Links

    Wave-particle duality of light

    In the late 17th century Sir Isaac Newton had advocated that light was particles, but Christiaan Huygens took an opposing wave approach. Thomas Young's interference experiments in 1801, and François Arago's detection of the Poisson spot in 1819, validated Huygen's wave models. However the wave model was challenged in 1901 by Planck's law for black-body radiation. Max Planck heuristically derived a formula for the observed spectrum by assuming that a hypothetical electrically charged oscillato...

    Wave-particle duality of matter

    The contradictory evidence from electrons arrived in the opposite order. Many experiments by J. J. Thomson,: I:361 Robert Millikan,: I:89 and Charles Wilson: I:4 among others had shown that free electrons had particle properties, for instance the measurement of their mass by Thompson in 1897. In 1924 Louis de Broglie in his PhD thesis Recherches sur la théorie des quanta introduced his theory of electron waves. He suggested that an electron around a nucleus could be thought of as being a stan...

    Before proceeding further, it is critical to introduce some definitions of waves and particles both in a classical sense and in quantum mechanics. Waves and particles are two very different models for physical systems, each with an exceptionally large range of application. Classical waves obey the wave equation; they have continuous values at many ...

    The electron double slit experiment is a textbook demonstration of wave-particle duality.A modern version of the experiment is shown schematically in the figure below. Electrons from the source hit a wall with two thin slits. A mask behind the slits can expose either one or open to expose both slits. The results for high electron intensity are show...

    While electrons were thought to be particles until their wave properties were discovered; for photons it was the opposite. In 1887, Heinrich Hertz observed that when light with sufficient frequency hits a metallic surface, the surface emits cathode rays, what are now called electrons.: 399 In 1902, Philipp Lenard discovered that the maximum possibl...

    Normally angular momentum is considered to be a particle-like property, for instance a spinning top. However, light waves can have angular momentum when they form a vortex, as illustrated in the Figure. Electrons waves with angular momentum have also been produced, with up to a thousand angular momentum quanta.These matter waves will diffract and i...

    In a "which way" experiment, particle detectors are placed at the slits to determine which slit the electron traveled through. When these detectors are inserted, quantum mechanics predicts that the interference pattern disappears because the detected part of the electron wave has changed (loss of coherence). Many similar proposals have been made an...

    R. Nave. "Wave–Particle Duality". HyperPhysics. Georgia State University, Department of Physics and Astronomy. Retrieved December 12, 2005.
    "Wave–particle duality". PhysicsQuest. American Physical Society. Retrieved August 31, 2023.
    Mack, Katie. "Quantum 101 – Quantum Science Explained". Perimeter Institute for Theoretical Physics. Retrieved August 31, 2023.
  4. The de Broglie–Bohm theory, also known as the pilot wave theory, Bohmian mechanics, Bohm's interpretation, and the causal interpretation, is an interpretation of quantum mechanics. It postulates that in addition to the wavefunction , an actual configuration of particles exists, even when unobserved.

  5. The wave theory of light, broadly successful for over a hundred years, had been challenged by Planck 's 1901 model of blackbody radiation and Einstein 's 1905 interpretation of the photoelectric effect. These theoretical models use discrete energy, a quantum, to describe the interaction of light with matter.

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