If λ = hc/E, what is dλ? Can you find the differential?ProPatto16 said:[tex]\Delta[/tex][tex]\lambda[/tex]=([tex]\Delta[/tex]E/E)[tex]\lambda[/tex]
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How do you figure?ProPatto16 said:ah okay just wasnt sure what you were asking.
d[tex]\lambda[/tex]/dE would be [tex]\lambda[/tex]d[tex]\lambda[/tex] = hc/E dE
which would be 1 = -hc/E2 ?
Not quite. Δλ = -(hc/E2) ΔE. Now can you find Δλ/λ ?ProPatto16 said:no wait. d[tex]\lambda[/tex] wouls be a rate of change so then [tex]\Delta[/tex][tex]\lambda[/tex] = -hc/E2 ?
This is correct except you need E2 in the denominator.ProPatto16 said:oh gee. i feel so dumb -.- this should be so easy.
the notation i use for this differential would be:
hc/E dE
= hcE-1 dE
This is not. You just can't drop the dE.= (-1)hcE-2
= (-hc)/E2
"<" means "less than"; "<<" means "much less than"; "<<<" means "even less than that".ProPatto16 said:whats the relevance of |[tex]\Delta[/tex][tex]\lambda[/tex]/[tex]\lambda[/tex]|<<1?
does << mean less than? or something else?
Unless there is more.ProPatto16 said:So it's all good then :)
The particle uncertainty principle, also known as the Heisenberg uncertainty principle, is a fundamental principle of quantum mechanics that states that it is impossible to simultaneously know the exact position and momentum of a particle. This principle arises from the wave-particle duality of quantum particles, which means that they can exhibit both wave-like and particle-like behavior.
The particle uncertainty principle has a significant impact on our understanding of particles because it sets a limit on the precision with which we can measure their properties. This means that there will always be some degree of uncertainty in our knowledge of a particle's position or momentum, and this uncertainty increases as the precision of our measurements increases.
No, the particle uncertainty principle is not a limitation of our measurement tools. It is a fundamental property of quantum particles that cannot be overcome. This means that even with perfect measurement tools, we would still encounter this uncertainty in our measurements.
The particle uncertainty principle is closely related to the observer effect, which is the idea that the act of observing a system can affect its behavior. In the case of the particle uncertainty principle, the act of measuring a particle's position or momentum inevitably disturbs the particle, making it impossible to know both properties with certainty.
While the particle uncertainty principle is a fundamental property of quantum particles, it is not typically applicable to macroscopic objects. This is because the effects of quantum mechanics are generally only observable at the subatomic level. However, some experiments have shown that the principle can also apply to larger objects, such as molecules, under certain conditions.