Heisenberg Uncertainty Principle (1 Viewer)

[milton]

Why do so many textbooks confuse the Heisenberg Uncertainty Principle with the observer effect? The uncertainty principle in quantum mechanics is sometimes erroneously explained by claiming that the measurement of position necessarily disturbs a particle's momentum eg by using a high frequency photon to measure the position of an electron, we disturb its momentum and vice versa

it's not because we don't have precise enough technology, not because we don't know where the electron is, its becuase the electron ITSELF doesn't know where it is. as a result of wave-particle duality and the inherent non-determinism in quantum mechanics

how ironic that einstein explained the photoelectric effect, founding quantum theory, yet later exclaiming that "God does not play dice"

 

[macoboi]

how ironic that einstein explained the photoelectric effect, founding quantum theory, yet later exclaiming that "God does not play dice"

Not very, in saying that, einstein was referring to the fact that quantom theory was nowhere near complete, that there must be a better answer than the probability of where an electron is.

 

[shinji]

how about this? =D

http://www.youtube.com/watch?v=4W9tHxtsGys


watch that. lmao,,
=]

 

[samwell]

wait the uncertainty principle when applied to bohr's atomic model does not really make sense. Bohr postulated that the eletron must follow the quantam eqn{circumference*momentum =nh} and the application of planck's quantisation principle to the atomic model. The major problem is that the fundamental principle of Heisenberg is that if we know momentum we dont noe its position and vice versa. so how come the can use the quantam eqn of bohr's postulate? and further how do we know the position of the electron in a certain energy level? anybody with a concise explanation?

 

[Captain Gh3y]

wait the uncertainty principle when applied to bohr's atomic model does not really make sense. Bohr postulated that the eletron must follow the quantam eqn{circumference*momentum =nh} and the application of planck's quantisation principle to the atomic model. The major problem is that the fundamental principle of Heisenberg is that if we know momentum we dont noe its position and vice versa. so how come the can use the quantam eqn of bohr's postulate? and further how do we know the position of the electron in a certain energy level? anybody with a concise explanation?

nah ur actually right, well spotted

turns out if u apply the UP to the Bohr Model the uncertainty is big enough taht u don't even know if the electron is attached in to the atom anymore (greater than ionisation energy)

 

[Captain Gh3y]

here's the maths

Calculate Δp, ΔE for an electron within a distance a₀ of the nucleus of a hydrogen atom, i.e. in the first Bohr orbit.
Δx = 0.53x10^-10 m so Δp ≥ ħ/2 Δx = 10^-24 kgms-1.

Now since E=p^2/2m this uncertainty in p corresponds to an uncertainty in E.
ΔE/Dp ~ ΔE/dp = p/m. So ΔE=pΔp/m.

Now for an electron in the first Bohr orbit (n=1)
the momentum p = ħ/a₀ = 2x10^-24 kgms-1.

Then ΔE ~ 14eV! This is greater than the ionisation energy of H. So we don’t know if the electron is bound anymore!

 

[samwell]

so basically when we apply Heisenberg's principle to Bohr's model we do get different and contradicting natures of the electron. The electron is such a bloody complex negatively charged particle. Can u explain the Zeeman and its anomolous state in regards to the unceratinty principle.

 

[Captain Gh3y]

Well it's basically just that the Bohr model isn't correct (just a good approximation for hydrogen-like atoms), it was replaced by a fully Quantum Mechanical model which is based on solving the 3d time dependent schroedinger equation

the idea is you can't talk about exact energies, only probabilities

good q to ask ur teacher

I can't really explain the Zeeman effect properly since I haven't done atomic physics

Basically there can be several electrons in one energy state but with different quantum numbers, and since electrons with different quantum numbers will interact differently with the magnetic field, the presence of a magnetic field splits up the energy states.

I can't remember if quantum numbers are mentioned in Q2Q or not
In the qm model of the atom they're like constants when you solve the schroedinger equation that describe a particular energy state uniquely

states with the same energy are said to be "degenerate", so the zeeman effect breaks up degenerate energy states

the pauli exclusion principle says that no 2 electrons can have the exact same combination of quantum numbers