The h Bar

user228700

1:23 AM

Hi everyone :-)

user228700

I have a quick question: when deriving the relation b/w the wavelength of a substance (not light) and its momentum, why can't I equate $h\nu$ to $1/2mv^2$ instead of $mc^2$?

0celo7

what is $h\nu$ supposed to be for a general object?

user228700

Yeah, that's not so clear to me, but $\nu$ is the frequency of the matter wave. $h\nu$ is technically how much energy one quanta of the wave has but yeah, in case of matter waves :/

0celo7

that only works for photons

Andras Deak

hey

@0celo7 not exactly

ACuriousMind

1:29 AM

@Kaumudi When you say "wavelength of a substance", do you mean the de Broglie wavelength assoicated to the "matter wave" of a particle?

user228700

@ACuriousMind Yes.

Andras Deak

de Broglie's "matter wave" hypothesis stated that finite-mass particles can also be described by a wave, the wavelength of which obeys p=h/lambda

ACuriousMind

Also, when you say you equate $hv$ to $mc^2$, is the $m$ the rest mass or the "relativistic mass"?

0celo7

Why in quotes?

user228700

@ACuriousMind The rest mass...in case of matter waves.

Andras Deak

1:31 AM

Although this is usually formulated in terms of momenta. Will that give you $h \nu=mv^2/2$ ?

user228700

I'll tell u what my textbook has done: it has arrived at $hc/\lambda=p$ in the case of photons and then it has written "by analogy, since matter waves have velocity $v$, we have $hc/\lambda=mv$"

Andras Deak

that's the usual approach, and "by analogy, we have" should probably be "let's hypothesise because why not"

0celo7

that's physics for you

Andras Deak

:P this is even worse

ACuriousMind

@Kaumudi Okay. Where are you "equating $h\nu$ to $mc^2$" there?

Andras Deak

1:33 AM

and de Broglie didn't know that you can do the double-slit experiment with fullerene molecules and stuff

0celo7

you can do double slit with fullerenes?

user228700

@ACuriousMind $h\nu=mc^2$ implies $hc/\lambda=mc^2$ implies $h/\lambda=mc$ implies $\lambda=h/p$

user228700

Then, "by analogy" ._. That's what my textbook has done, I mean.

Andras Deak

@0celo7 yup

what's more, they'll produce an interference pattern

ACuriousMind

If you're asking why you can't attempt a "derivation" for matter waves by putting their kinetic energy there, then the answer is that you can't actually derive the de Broglie wavelength in this way. At this level, it's a postulate that the $\lambda = h/p$ also holds for matter waves.

Andras Deak

1:36 AM

last time I checked it was mildly anecdata, but I'm fairly certain it's real

0celo7

@AndrasDeak well, yes

what else would double slit be?

user228700

@ACuriousMind Yes, that is what I was asking, and OK, I see...

Andras Deak

@0celo7 well you can do a double-slit experiment with bowling balls, just don't expect a strong evidence of wave-like behaviour:D I just wanted to be sure, suspecting that some...hmmm...pedantic people might be around

user228700

But there's that whole thing where "photons don't have any rest mass" and all, so should I just look over that if I don't want to dig too deep into this? I mean, is understanding that key to understanding this concept..?

ACuriousMind

@Kaumudi To understanding what concept?

Andras Deak

1:38 AM

Wave–particle duality of C$_{60}$ molecules

0celo7

@ACuriousMind do you like my new avatar?

Andras Deak

@Kaumudi don't dig too deep, it's a completely arbitrary assumption that shouldn't be taken too seriously

it has fun stuff, such as predicting the Bohr radius, if I recall correctly

user228700

@ACuriousMind How the equation works, I guess, for photons.

ACuriousMind

@0celo7 You still appear as the deformed cat to me

user218912

@0celo7 i think it doesn't suit you but it's ok i guess

Andras Deak

1:40 AM

it's a pretty feminine feline if you ask me (doesn't make it good nor bad, just noting)

0celo7

@ACuriousMind f5?

@AndrasDeak Well I'm a girl, so

user218912

huh?

Andras Deak

So why not a cat map?

0celo7

it's an ocelot kitten

ACuriousMind

@AndrasDeak Eh, you can see that $h/p$ is e.g. the wavelength with which electrons fired at something diffract, it should be taken seriously, and in actual quantum mechanics it's clear as day that a momentum eigenstate is a plane wave with wavelength $h/p$.

Andras Deak

1:42 AM

meh:P

those are specific results of QM, and have theoretical basis

user228700

O.o

Andras Deak

de Broglie's hypothesis always came across as pretty ad hoc to me

0celo7

I condone this message ^

Er, approve of

Andras Deak

I'll take anything positive

ACuriousMind

@Kaumudi I'm not sure what confuses you - the equation $\lambda = h/p$, and also the equation $h\nu = E$ works for all object. It's just that $p$ and $E$ are different for massless and massive particles

user228700

1:45 AM

So...is it OK if I don't understand why we're allowed to use an $m$ for photons while deriving that relationship?

user228700

@ACuriousMind Can u tell me how they're different, pls?

ACuriousMind

@AndrasDeak Sure, the original de Broglie hypothesis was, and I'm puzzled why we still teach it in that way. But what it says, i.e. its statement about the wavelength of a matter wave, is correct and not at all arbitrary or not serious

@Kaumudi $E= pc$ for a photon, $E=\sqrt{mc^2 + p^2c^2}$ for a massive particle.

Transcript for