How can the amplitude and wavelength of a matter wave be visualized???

Question

If particles behave as waves at times, what would the waves look like in 2D/3D? Is it even possible to visualize them at all?

Answer 1

It's possible to visualize the wavelength because you can think of sinusoidal variations in ANYTHING existing and moving along.

However, it's harder with the amplitude, because these waves really exist in an abstract space, rather than in our own space. The CONSEQUENCES can of course be seen, for example in thinking about the two slit experiment, and seeing where the two "radiating sources" interfere constructively or destructively. If it were possible to double one of these amplitudes, while leaving the other unaltered, you could still sketch out the consequences you'd expect by adding those separate interfering effects together.

Another thing that makes it hard to visualize matter waves associated with a given particle, say, is that they don't actually move with the particle. You may know that the particle actually moves with the "group velocity" of a group of waves with wavelengths close to that given by the de Broglie wavelength formula. A DEFICIENCY of the usual, non-relativistic treatment of this is that there is an INESCAPABLE factor of two difference between the individual particle wave function's velocity and the GROUP VELOCITY.

Does this make sense? My position is : "NO, IT'S PHYSICALLY ABSURD." It also distorts de Broglie's thinking and vision. Because of the way that introductory quantum mechanics is taught, it is often not appreciated that de Broglie's great insights came about because of a deep and abiding belief in special relativistic invariance. It was HE who first introduced and investigated the concept of the group velocity in quantum mechanics. And guess what he showed? : that the GROUP VELOCITY of matter waves MOVES WITH THE PARTICLE'S SPEED!

As he himself said. "What could be more beautiful, and yet more natural and required. Energy moves with the group velocity, Einstein showed us that energy and mass (including rest mass) were equivalent, and so the energy that's equivalent to the mass moves with that mass!"

When I contemplate the simplicity and clarity of that last conclusion, it makes me sahke my head in disappointment that de Broglie's work is so BADLY represented intoday's physics textbooks --- if at all.

Live long and prosper.

Answer 2

properly each wave is persevering with in a standing wave, so there is in straight forward terms one fee. yet while the frequency of the wave ameliorations once you're staring at it, so does the fee for wave amplitude. The fee of the amplitude of a wave isn't on the subject count of the flexibility of the wave. because of the fact a wave with a protracted wavelength might have quite some power yet might have an identical amplitude of a wave with a smaller wavelength and smaller fee of power. The power of the wave is barely based on the wavelength.

Answer 3

for real, waves cannot be seen with the naked eye. but abstractly, waves are usually drawn in sinusoidal (sine waves). on that note, its usually 2D.
Amplitude is measured from origin to crest or trough (the origin is where the wavepoint is zero). Wavelength is measured from crest to crest or trough to trough, meaning from peak to peak of the wave. these things vary depending on the given frequency, but the amplitude is usually constant.