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

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

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