De Broglie wave equation - Derivation by SK

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  • ABCC Australia 2015 www.new-physics.com

    WAVE-PARTICLE EQUATIONSK Deriving de Broglies

  • ABCC Australia 2015 www.new-physics.com

    de Broglie Wave Equation

    Let us have a fresh look at

    de Broglies wavelength equation which is:

    = /

    In the earlier days of de Broglies theory, the electron () is the main particle in concern. So we start our discussion with the electron.

    The Eskade Postulate 01 stated that all particle motions are instigated by phonons or photons, be it electrons or any other matter.

    = /

    = /

    = /

  • ABCC Australia 2015 www.new-physics.com

    Eskade Carrier Postulate

    By the carrier postulate (Eskade postulate 01), and by the principle of the conservation of energy, the energy of the moving electron comes entirely from the incorporated photon. So the energy of the composition resides with photons:

    Electron kinetic energy = Photon kinetic energy

    122 =

    122

    2 = 2

    122 =

    122

    Kinetic energy of particle

    Kinetic energy of photon

    2 = 2

    Eliminating from both sides

  • ABCC Australia 2015 www.new-physics.com

    Momentum of Wave

    Now = is the momentum of the electron; and 2 = is the energy of the photon. So:

    2 = 2

    Becomes: =

    Swapping the relevant items, we have:

    / = /

    This is in accordance with the principle of energy conservation. The photon is still vibrating at the same frequency.

    2 = 2

    2 x Kinetic energy of photon

    Planck energy of photon

    / = /

    = = is the momentum of the electron

  • ABCC Australia 2015 www.new-physics.com

    The de Broglie Wave Equation

    The equation / gives us the wavelength :

    =

    Thus the de Broglie wavelength equation is:

    =

    Which was proposed by de Broglie in 1924.

    / = /

    = /

  • ABCC Australia 2015 www.new-physics.com

    Summary of de Broglie particle-waves.

    1) An electron can move because of carrier particles such as photons or phonons.

    2) A moving electron is wave-like because of the oscillating carrier.

    3) The momentum of the electron is the momentum of the carrier.

    4) The kinetic energy of the electron is the energy of the carrier.

    5) The wavelength of a moving electron is the shortened wavelength of the carrier because of the heavier electron.

    Louis de Broglie (1892-1987)

  • ABCC Australia 2015 www.new-physics.com

    Summary of Eskade Postulates

    1) Particles are moved by carrier particles mainly photons or phonons.

    2) The vibrating nature of matter are due to the photons or phonons as in de Broglie waves.

    3) Photons retain their vibration in free or bound state, leading to the principle of energy and momentum conservations in low energy cases.

  • ABCC Australia 2015 www.new-physics.com

    CIRCULAR MOTIONThis article is related to:

    ABCC

    Wave-particle equationde Broglie Wave EquationEskade Carrier PostulateMomentum of WaveThe de Broglie Wave EquationSummary of de Broglie particle-waves.Summary of Eskade PostulatesCircular motion

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