We know that electrons have a dual nature just like EM waves(of course all the material are said to have dual nature; noticeable or not). So looking at wave nature of electron and comparing this with photons, is it possible to make it's kinetic energy equal to zero?
The group velocity of an electron can be zero. It is a standing wave in this case. But according to the Heisenberg principle you cannot define both momentum and position precisely. If you want a momentum of exactly zero and not a momentum spectrum centered around zero (standing wave), your electron would have the wavelength infinity and would be delocalized across the entire universe.
The group velocity of an electron can be zero. It is a standing wave in this case. But according to the Heisenberg principle you cannot define both momentum and position precisely. If you want a momentum of exactly zero and not a momentum spectrum centered around zero (standing wave), your electron would have the wavelength infinity and would be delocalized across the entire universe.
Dieter,
Great answer, almost exactly right, with the small obvious proviso however that the Universe is not infinite, and hence you just cannot have momentum exactly zero (calculation of the ground momentum being quite straightforward).
Interestingly, an immobile electron situation would, in temperature terms, be absolute zero (which of course could never be reached anyway, even in an infinite universe, owing to Heisenberg effects. The Heisenberg effects would by the way always be on the 0+ (positive) side of the scale - the Kelvin etc. scales being only linear approximations of an actually logarithmic scale, with absolute zero thus being, in fact, minus infinite, so that, say, -273.151 Kelvin cannot exist)
@Dieter As a reflection to your "explanation", I address to analyze this amazing situation: How wil you explain the momentum and position data of electron located inside a high enough and very spatially narrow quantum dot?
Then its position is localized inside the dot almost exactly with any accuracy, and at the same time, its momentum is also fixed? Moreover, this electron can never be spread "to infinity" as it can not abandon the dot well! - So, there is some thing wrong with the Heisenberg uncertainty...
@H_Chris_Ransford
Only a small remark: the notion of tempereature has nothing to do to a unique separately chosen electron... It is a collective effect of many particles, being only classically( not quantum and relativistically) proportional to their average kinetic energy.
Sincerely regards!
P.S. Somebody within this RG link in the obscured way voted "down" my modest question to Mr. Dieter above which, being left by this person with no comment, I consider as a slightly arrogant style of discussion.
Sorry for the honest truth told here.
Anatolij,
Maybe you misunderstood me.
What I'm saying - say, within a gas at any specific temperature, you can easily assemble sub-collections - sub-ensembles - of molecules whose overall 'temperature ' would come out at any temperature you would want to set and choose beforehand. For instance, take a gas at , say, plus one hundred degrees - you can "ohne weiteres" assemble from that macro-ensemble a sub-collection of particles whose properties and characteristics, taken together and statistically measured together, would wind up being at, say, minus 100 degrees.
PS - don't worry about the downvotes, they're inevitable and often are given with people with an agenda - the folks who just know what the truth is.
@H Chris Ransford
Yes, I have catched your comment, it is right.
P.S. Dear Chris, thanks for understanding!
Sincerely,
regards!
@Krzysztof Bohdan
Respect, -- your comment really unveils a very subtle matter of elementary particles physics which is often ignored by physicists, even very good... One can predict that this aspect will play an important role in the future physics.
@Kryzysztof Bohdan and others...
Thank u for ur elaborate discussions here sirs.
Can I get reference material regarding ur statement "When an electron has zero kinetic energy, it ceases to be an electron" ?
@Krzysztof Bohdan
Yes, nice calculations, yet it is still important to mention that this model is strongly non-relativistic (!) and the derived uncertainty condition is related only to the space-momentum, and nothing similar there was derived in the relativistic case, saying nothing about the time-energy relationship, which in contrary stems from relativity theory...
Regards!
@Ana María
You are great! Happy and Merry Season's Holidays to You!
The discussions are very interesting to look back at!
Thank you for your scientific and inspiring answers..
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