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"DERIVATION" OF THE DE BROGLIE RELATION FROM THE DOPPLER EFFECT

Crawford, Frank S.

In this note we assume that all particles have wave properties and hence must exhibit a Doppler shift when they reflect from a massive slowly receding mirror. We then show that particles must satisfy the de Broglie relation.

Oct 1, 19800 citations

Interpretation of de Broglie waves: At what time does a massive particle obtain the properties of a wave?

Masanori Sato, Hiroki Sato

Physics EssaysJun 1, 20123 citations

The Doppler Origin of de Broglie Waves

R. L. Collins

APSOct 1, 19980 citations

Phase waves in finite potentials: the harmonic oscillator and the hydrogen atom

John M. Masnovi

de Broglie’s concept of particles as sources of phase is extended to the analysis of systems in which the potential is not constant. The treatment assumes that the phase information propagates as waves according to classical electrodynamics including reflection with phase changes from potential energy barriers. The energies and weighting functions in such cases are obtained by comparison of the phase of the accelerated particle relative to the phases of reflections from the change in potential. Application to the chemically interesting systems of the harmonic oscillator and hydrogen atom are considered using the time evolution of the relative phases of the reflected de Broglie phase waves, whereby the weighting functions are obtained from the distance dependence of the phase differences between the reflections and the source. This is accomplished conveniently by taking time derivatives of the relative de Broglie phases and considering the periodicity of the motion. Optimum trajectories are determined by minimization of the action 2i(mv2-r∂V/∂r)/ħγ which depends on the potential V and the velocity v. The treatment leads to the Newtonian force law for circular orbits and affords the same energies as derived using the Schrödinger equation.de Broglie’s concept of particles as sources of phase is extended to the analysis of systems in which the potential is not constant. The treatment assumes that the phase information propagates as waves according to classical electrodynamics including reflection with phase changes from potential energy barriers. The energies and weighting functions in such cases are obtained by comparison of the phase of the accelerated particle relative to the phases of reflections from the change in potential. Application to the chemically interesting systems of the harmonic oscillator and hydrogen atom are considered using the time evolution of the relative phases of the reflected de Broglie phase waves, whereby the weighting functions are obtained from the distance dependence of the phase differences between the reflections and the source. This is accomplished conveniently by taking time derivatives of the relative de Broglie phases and considering the periodicity of the motion. Optimum trajectories are determined by minimization of the action 2i(mv2-r∂V/∂r)/ħγ which depends on the potential V and the velocity v. The treatment leads to the Newtonian force law for circular orbits and affords the same energies as derived using the Schrödinger equation.

Nov 26, 20170 citations

Quantum Mechanics without Schrödinger: Bohmian Mechanics of de Broglie Waves for a Particle in a Box

John M. Masnovi

A formulation is proposed for the behavior of a particle in a box based on two assumptions: (1) particles have an associated phase which changes periodically with time as defined by de Broglie, and (2) the transmission of phase information follows optical principles, including reflection at potential boundaries and relativistic Doppler effects. This approach defines optimal trajectories by matching the phase of a source and its reflections. The momentum of the particle is guided by a de Broglie wave which follows the equation R exp {i[w0 (1-v^2/c^2)^-1/2][(t - vz)/c^2]} cos {[w0(1-v^2/c^2)^-1/2/c](vt-z)} This wave is generated by reflections occurring an even number of times, the phase and amplitude of which correspond to Lorentz transforms relative to the time and position, respectively. Nodes are produced by reflections occurring an odd number of times, which can be conceived to generate a wave traveling in the opposite direction and shifted by a phase constant π. Application to an individual particle in an infinite potential well affords the same results for energies and nodes as derived by the Schrödinger equation.A formulation is proposed for the behavior of a particle in a box based on two assumptions: (1) particles have an associated phase which changes periodically with time as defined by de Broglie, and (2) the transmission of phase information follows optical principles, including reflection at potential boundaries and relativistic Doppler effects. This approach defines optimal trajectories by matching the phase of a source and its reflections. The momentum of the particle is guided by a de Broglie wave which follows the equation R exp {i[w0 (1-v^2/c^2)^-1/2][(t - vz)/c^2]} cos {[w0(1-v^2/c^2)^-1/2/c](vt-z)} This wave is generated by reflections occurring an even number of times, the phase and amplitude of which correspond to Lorentz transforms relative to the time and position, respectively. Nodes are produced by reflections occurring an odd number of times, which can be conceived to generate a wave traveling in the opposite direction and shifted by a phase constant π. Application to an individual particle in an infinite potential well affords the same results for energies and nodes as derived by the Schrödinger equation.

Sep 21, 20170 citations

The de Broglie wave derivation for material particle diffraction re-examined: a re-derivation without matter waves

Robert Ter Bush

Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimentoDec 1, 19850 citations

’’Derivation’’ of the de Broglie relation from the Doppler effect

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’’Derivation’’ of the de Broglie relation from the Doppler effect

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