Matter wave - relationship between broglie wavelength, wavelength

[Deathnote777]

Homework Statement

1. fh stands for energy of a particle. But what is included in the energy ? K.E. of the particle only ?
1.1. If fh is the K.E only, then I have a question. λ=h/p --> fλ=fh/mv --> mv^2 = fh. It is strange that fh = mv^2 but not 1/2 mv^2.

2. Is broglie wavelength equivalent to wavelength ? (e.g. Consider a Infrared light, does its wavelength same as the broglie wavelength of its photon ? )
3. What does it exactly mean when we talk about the frequency of electron/photon ?

I am really confused about the relationship between broglie wavelength, wavelength, Energy(fh), K.E. and frequency of the particles. I hope you can clear my concept , Thanks !

Homework Equations

λ=h/p

The Attempt at a Solution

 

[sankalpmittal]

Homework Statement

1. fh stands for energy of a particle. But what is included in the energy ? K.E. of the particle only ?
1.1. If fh is the K.E only, then I have a question. λ=h/p --> fλ=fh/mv --> mv^2 = fh. It is strange that fh = mv^2 but not 1/2 mv^2.

No !

λ=h/p
And , K.E.=p²/2m and K.E.=fh

2. Is broglie wavelength equivalent to wavelength ? (e.g. Consider a Infrared light, does its wavelength same as the broglie wavelength of its photon ? )

No. Their contexts are different. Although dimensionally they are equivalent.

3. What does it exactly mean when we talk about the frequency of electron/photon ?

Energy of photons = n*h*frequency of photon

Think from here.

I am really confused about the relationship between broglie wavelength, wavelength, Energy(fh), K.E. and frequency of the particles. I hope you can clear my concept , Thanks !

 

[TSny]

1.1. If fh is the K.E only, then I have a question. λ=h/p --> fλ=fh/mv --> mv^2 = fh. It is strange that fh = mv^2 but not 1/2 mv^2.

fλ equals the phase velocity of the deBroglie waves. The phase velocity of the waves does not equal the velocity of the particle. But you an show that the group velocity of the deBroglie waves does equal the velocity of the particle.

 

[Deathnote777]

fλ equals the phase velocity of the deBroglie waves. The phase velocity of the waves does not equal the velocity of the particle. But you an show that the group velocity of the deBroglie waves does equal the velocity of the particle.

Thanks. Now, consider a photon. λ=h/p. fλ = E/p. What should fλ be ? My book says it is c. But why ? Isn't fλ the group velocity
broglie wavelength has same value as wavelength, right ? Is it true that particle has only broglie wavelength but not wavelength ?
And is there phase velocity in quantum physics ? Isn't it only exist in classical one ?

No !

λ=h/p
And , K.E.=p²/2m and K.E.=fh

No. Their contexts are different. Although dimensionally they are equivalent.
Energy of photons = n*h*frequency of photon

Think from here.

How can we calculate the frequency of the particle? phase velocity / broglie wavelength or particle velocity / broglie wavelength ?

 

[bossman27]

That's actually the first time I've looked this up, but here's from wikipedia:
"The group velocity is often thought of as the velocity at which energy or information is conveyed along a wave. In most cases this is accurate, and the group velocity can be thought of as the signal velocity of the waveform. However, if the wave is traveling through an absorptive medium, this does not always hold. Since the 1980s, various experiments have verified that it is possible for the group velocity of laser light pulses sent through specially prepared materials to significantly exceed the speed of light in vacuum. However, superluminal communication is not possible in this case, since the signal velocity remains less than the speed of light. It is also possible to reduce the group velocity to zero, stopping the pulse, or have negative group velocity, making the pulse appear to propagate backwards. However, in all these cases, photons continue to propagate at the expected speed of light in the medium."

In short, the possible variations in group velocity are produced by the absorptive properties of the medium (i.e. absorption and emission of photons by other particles); the individual photons, however, always have a velocity of c.

 

[Deathnote777]

That's actually the first time I've looked this up, but here's from wikipedia:
"The group velocity is often thought of as the velocity at which energy or information is conveyed along a wave. In most cases this is accurate, and the group velocity can be thought of as the signal velocity of the waveform. However, if the wave is traveling through an absorptive medium, this does not always hold. Since the 1980s, various experiments have verified that it is possible for the group velocity of laser light pulses sent through specially prepared materials to significantly exceed the speed of light in vacuum. However, superluminal communication is not possible in this case, since the signal velocity remains less than the speed of light. It is also possible to reduce the group velocity to zero, stopping the pulse, or have negative group velocity, making the pulse appear to propagate backwards. However, in all these cases, photons continue to propagate at the expected speed of light in the medium."

In short, the possible variations in group velocity are produced by the absorptive properties of the medium (i.e. absorption and emission of photons by other particles); the individual photons, however, always have a velocity of c.

I don't know much actually. But fλ is not the individual speed of photon, isn't it ? fλ should be the phase velocity, is it right ?

 

[bossman27]

Yes, that's correct, the velocity of a particle is the group velocity of its matter wave. For a massive particle, the phase velocity actually exceeds c... but, the phase velocity of a photon is equal to c, the same as its group velocity.

In relativistic terms you can write it this way:

v_{p} = \frac{E}{p} = \frac{\gamma m c^{2}}{\gamma m v_{g}} = \frac{c^{2}}{v_{g}} = \frac{c}{\beta}

Where \beta is the ratio of the particles velocity to c.

 

[Deathnote777]

Yes, that's correct, the velocity of a particle is the group velocity of its matter wave. For a massive particle, the phase velocity actually exceeds c... but, the phase velocity of a photon is equal to c, the same as its group velocity.

In relativistic terms you can write it this way:

v_{p} = \frac{E}{p} = \frac{\gamma m c^{2}}{\gamma m v_{g}} = \frac{c^{2}}{v_{g}} = \frac{c}{\beta}

Where \beta is the ratio of the particles velocity to c.

Thanks, that means light is a special case in which phase velocity = individual one

 

[Deathnote777]

How about

Isn't fλ the group velocity
broglie wavelength has same value as wavelength, right ? Is it true that particle has only broglie wavelength but not wavelength ?
And is there phase velocity in quantum physics ? Isn't it only exist in classical one ?

How can we calculate the frequency of the particle? phase velocity / broglie wavelength or particle velocity / broglie wavelength ?