What is the Amplitude of a Particle? Understanding Photon Waves and Displacement

[Simon43254]

If a photon can be graphically demonstrated as a wave with amplitude x, what does the amplitude correspond to on a particle? Is it, it's displacement from its mean position at a given time?

 

[jtbell]

In quantum mechanics, the amplitude (at some location) of the wave that represents a particle corresponds to the probability of finding the particle at or near that location. More specifically,

P(x) = \Psi^*(x) \Psi(x)

where \Psi is the wave function, which is generally complex, and P is the probability density.

 

[Simon43254]

Ok, on the quantum side that makes sense. So what about the classical?

 

[Studiot]

You need to know that the 'wave function' is not truly oscillatory like for example y=sin(x).

The wave function JT refers to is the solution of Schrödinger's 'wave' equation, which is not really a wave equation at all it is called that because it is similar to the true wave equation which has an oscillatory solution y=sin(x).

 

[Academic]

Classically, the amplitude of an EM wave is the magnitude of the E-field (by convention).

 

[LostConjugate]

Ok, on the quantum side that makes sense. So what about the classical?

Classical Mechanics is designed to work with only a large number of particles. It does not apply to a small number of particles or a single particle.

When developing classical physics we worked with objects like apples, large metal objects, people, etc. All things which are a large collection of particles. Even in QM the expectation values (which describes classical results) do not give accurate information about a small number of particles.

 

[jtbell]

Ok, on the quantum side that makes sense. So what about the classical?

Classical physics doesn't contain the notion of "photons." In classical physics, light is purely a electromagnetic wave phenomenon. Nor does it contain the notion of particles having wave-like behavior.