Particle-Wave Duality of Elementary Particles

[Daanikus]

Hi, I am new to this forum, and to physics in general.

I have been reading the basics of General Relativity and Quantum Mechanics but am yet to learn the mathematical side.

I am just trying to wrap my head around particle-wave duality and specifically, the wave quantifying of elementary particles.

When particles like leptons or quarks act as waves, how are these described? (In a basic sense). I am somewhat envisioning each particle having its own unique characteristics of frequency and amplitude within a quantum. Is this even close?

I understand light as frequency modulation, but is that all at a constant amplitude? And is the amplitude of a wave how we differentiate at all?

I apologize if that made no sense. As I say, only just embarking on this amazing field and I intend to pursue it indefinitely, so your answers won't go amiss! Thanks!

 

[wotanub]

Sometimes things act like particles, sometimes they act like waves.

As for how they are described, you can say a particle with momentum p has wavelength $λ = \frac{h}{p}$. h is the Planck constant. This was de Broglie's hypothesis.

Light has an amplitude with corresponds to intensity with just corresponds to how many photons there are.

Don't be afraid to read the overviews of the subject that include the mathematical details. They're the only way to truly understand what's going on.

 

[Daanikus]

Thanks for that.

So, when you have a stream of particles moving as a wave, they move as a single wave and its amplitude is the sum of all the energies?

Also, is it the wavefunction of the wave that determines the particle type?

 

[wotanub]

I don't think particles "move as a wave," it's just that a stream of particles can behave like a wave (e.g. exhibit interference) under certain conditions. You're probably thinking of the slit experiments.

The "amplitude" of a photon is really the amplitude of the electric field and when you square it you get the observable intensity, which goes up when there are more photons. Remember, the energy of a photon is determined by its frequency.

Wavefunctions and the wave-particle duality are two different concepts that have some connections that can be hand-waved, I probably shouldn't try to do it. Wavefunctions deal with probability amplitudes. If you square the amplitudes, wavefunctions give the probability to observe... something. It depends on what space the wavevector (state) is projected on. For example, a position-space wave function is the probability amplitude to observe at a certain position, momentum-space wavefunction tells you the probability amplitude for momentum, etc.

 

[etoman]

Hi

I recommend Leonard Susskind's lectures on Quantum Mechanics. (Part of a series of lectures on modern physics). Gives a good introduction to both the maths and the physical interpretation.

http://www.youtube.com/view_play_list?p=84C10A9CB1D13841

You can also view on iTunesU - which has the advantage of being able to view x1.5 and x2 if you want to move more quickly through some of the bits.

Best wishes

E

 

[wotanub]

Susskind's lectures are a good intro, but I recommend going through the classical mechanics ones before the quantum mechanics ones.

 

[Drakkith]

Thanks for that.

So, when you have a stream of particles moving as a wave, they move as a single wave and its amplitude is the sum of all the energies?

The wave properties that all particles have exists as a wavefunction that determines the probability of that particle being found in a certain location. This wave-like property exists at all times, even when the particle isn't moving. But, even though it isn't moving, if you make many accurate enough measurements, you will see that the particle will be found at different locations each time!

The adding together of particles to get one "larger" wave only works for bosons such as photons. Fermions cannot do this as they cannot occupy the same spot at the same time and thus can never add up in this way.

Also, is it the wavefunction of the wave that determines the particle type?

I'd say it's the reverse. The type of particle determines what its wavefunction will be.