![]() ![]() In a similar vein, we can imagine that Schrödinger followed a line of thought something like this: de Broglie proposes that any moving particle behaves like a wave whose wavelength depends on its mass and velocity. The energy of a particle is the sum of kinetic and. We start with the one-dimensional classical wave equation, Now we have an ordinary differential equation describing the spatial amplitude of the matter wave as a function of position. ![]() Here we follow the treatment of McQuarrie 1, Section 3-1. Very small particles do exhibit wave-like properties, and de Broglie’s hypothesis correctly predicts their wavelengths. The Time-Independent Schrdinger Equation. It is important physics, because it turns out to be experimentally valid. The illogical parts are the reason we call the result a hypothesis rather than a derivation, and the originality of the guesses and suppositions is the reason de Broglie’s hypothesis was new. characteristic action function, time enters from the denition of a classical momentum and. We have imagined that de Broglie found it by a series of imaginative-and not entirely logical-guesses and suppositions. We interpret this to mean that any mass, \(m\), moving with velocity, \(v\), has a wavelength, \(\lambda\), given by
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