Doubts about heisenbergs uncertainty principle.

[cartik]

Doubts about wave particle duality

I know that a wave packet is formed by superposition of several individual waves having different wavelength.And the resultant wave has varying amplitudes.And from these amplitudes we can find the likeliness of the object to be in that position.
My doubt is how can there be many waves of different wavelength associated with an object.
I mean by debroglies hypothesis λ=h/mv. So there should only be one long indefinite probability wave analogous to a cosine wave.(Where do so many waves come from?from the same object?)

Or is it this way-
I want to find the resultant wave packet of a baseball.
So i individually take all the atoms,electrons of the baseball, find their wavelength individually,and then add these waves(Superposition)?
then will i get a proper wave,with varying amplitudes?

 

[Naty1]

Hi Cartik:

I know that a wave packet is formed by superposition of several individual waves having different wavelength.

that's your answer. Any wave can be decomposed into constituent parts, just like '3' can be decomposed into 1+2, 1+1+1/2+1/2, etc,etc..

Remember things like: Sin2x =2SinxCosx [from high school trig]

see here for related descriptions:

http://en.wikipedia.org/wiki/Wave_packet

such as

A wave packet is a localized disturbance that results from the sum of many different wave forms.

What does your title have to do with your question?

 

[faen]

I know that a wave packet is formed by superposition of several individual waves having different wavelength.And the resultant wave has varying amplitudes.And from these amplitudes we can find the likeliness of the object to be in that position.
My doubt is how can there be many waves of different wavelength associated with an object.
I mean by debroglies hypothesis λ=h/mv. So there should only be one long indefinite probability wave analogous to a cosine wave.(Where do so many waves come from?from the same object?)

Or is it this way-
I want to find the resultant wave packet of a baseball.
So i individually take all the atoms,electrons of the baseball, find their wavelength individually,and then add these waves(Superposition)?
then will i get a proper wave,with varying amplitudes?

You can create any wave as a sum of smaller waves. Even a square formed wave. This is how: http://en.wikipedia.org/wiki/Square_wave

So why does two waves become one wave? Perhaps you should first ask yourself, what is a wave? A wave is something oscillating and then propagating in the perpendicular direction. Now you can try to imagine why waves of opposite amplitudes cancel each other out and why those of equal amplitude doubles. Then what does it look like when they cancel and contribute to each other on different positions? Then the result is what looks like another wave, since the particles themselves are still just oscillating up and down caused by forces.

Keep in mind that a baseball is a macroscopic object, and is not constituted by a single superposition.

 

[cartik]

But a wave packet is made by superposition of many matter waves right? So , for example we consider a wave packet of an electron, which is made up of many matter waves. My question is, that these 'many' matter waves having different wavelengths or phase are of what particles? (Using to debroglies hypothesis)...or is my understanding totally wrong?

 

[Maui]

My doubt is how can there be many waves of different wavelength associated with an object.

They are not real in the traditional sense, they live in phase space and cannot be observed(their existence is indirectly inferred). Also, 'object' is not something that can be unambiguously defined quantum mechanically.