What is the relationship between De Broglie frequency and energy in QM and QFT?

[ChAshutosh]

As we know de broglie wavelength is λ = h/p and f = E/h
λ = h/p
v/f = h/mv as f*λ=v

then

f = mv^2/h

but it should f = E/h and E=1/2*mv^2

 

[Suraj M]

When you say $$E= \frac{1}{2} mv^2 $$ you are considering only kinetic energy, do you think that, it is the only type of energy the body has, whose wave motion is also being is considered?

 

[bhobba]

Remember De-Broglies ideas are a mishmash of quantum and relatvistic ideas. Best to forget about them - they have long since been consigned to the dustbin of history. But since its relatvistic E is not the classical 1/2 mv^2:
http://hyperphysics.phy-astr.gsu.edu/hbase/debrog.html

Thanks
Bill

 

[Suraj M]

Bhobba, is there noway of achieving E = mv² by adding the energy due to SHM of each particle along the wave, to the KE?

 

[bhobba]

Bhobba, is there noway of achieving E = mv² by adding the energy due to SHM of each particle along the wave, to the KE?

I don't know what you mean by that.

Like most I have read about the De-Broglie theory and seen the equations. They are an inconsistent mish-mash eg what's the wavelength of a stationary particle - and by frame jumping you can always go to a frame where its stationary. Because of that I tend to not get worried about manipulations involving them - it's wrong anyway.

In QM the KE of a free particle is 1/2 mV^2 where V is the velocity operator.

Interestingly one can actually prove that from symmetry in QM - but that is another story.

Thanks
Bill

 

[Suraj M]

I don't know what you mean by that.

I mean the particles would have an extra amount of energy of $½m \omega^2 A^2$ can we use that?

 

[bhobba]

I mean the particles would have an extra amount of energy of $½m \omega^2 A^2$ can we use that?

You lost me.

Can you explain what your terms mean?

Thanks
Bill

 

[Suraj M]

The regular SHM terms! $\omega$ = 2$\pi /T$ ; A = amplitude of the wave

 

[bhobba]

I think you are trying to introduce concepts from the quantum harmonic occilator used in QFT. QFT is a whole new ball game not compatible with ordinary QM.

The energy in QM is actually based on the Galilaen transformations while QFT is based on the Lorentz transformations.

Thanks
Bill