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Kiley
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If velocity is delta position vs delta time and you know the velocity and change in time exactly why is it impossible to find the exact position of the electron? Same question for energy and position.
Welcome to the PF.Kiley said:If velocity is delta position vs delta time and you know the velocity and change in time exactly why is it impossible to find the exact position of the electron? Same question for energy and position.
Kiley said:If velocity is delta position vs delta time and you know the velocity and change in time exactly why is it impossible to find the exact position of the electron? Same question for energy and position.
Thank you, this is helpful in part.PeroK said:The Heisenberg Uncertainty Principle (HUP) is a statistical law. It applies to the measurements of, for example, momentum and position on an ensemble of identically prepared particles. If you prepare a large number of particles and measure, say, the momentum (at some time ##t##) for half of them and the position (at time ##t##) for the other half of them, then you will get a spread of measurements for both momentum and position. If you then take the standard deviation of these measurements, then they obey:
$$\sigma_x \sigma_p \ge \frac{\hbar}{2}$$
Where ##\sigma_x, \sigma_p## are the standard deviations for position and momentum respectively. One interpretation of this is that if you prepare a state with a well-defined momentum, then that state will have a relatively large spread of position measurements; and, vice versa.
The HUP doesn't say anything in particular about any single measurement of position or momentum of a particle.
Kiley said:View attachment 220427 C. Chemistry: a molecular approach, Tro.
Can you use mechanics equations for this? If not, why not?
Kiley said:Thank you, this is helpful in part.
Wow, thank you that's very cool. Are there any textbooks you can recommend specifically about this?PeroK said:PS It's also worth noting that in three dimensions, position and momentum in different directions are compatible, in the sense that:
##\hat{x}## commutes with ##\hat{p_y}## and ##\hat{p_z}## etc.
Where ##\hat{x}## represents the observable of position in the ##x## direction and ##\hat{p_y}, \hat{p_z}## represent the observables of momentum in the ##y, z## directions respectively.
Kiley said:Wow, thank you that's very cool. Are there any textbooks you can recommend specifically about this?
Awesome, thank you so much for your help, I was very nervous posting on here, so thank you for not being mean.PeroK said:I like Griffiths book on QM. Not everyone on PF would agree with that! But, it's a fairly standard undergrad introduction. But, you might be best to talk to your department about how much QM you are expected to learn.
The Uncertainty Principle, also known as Heisenberg's Uncertainty Principle, is a fundamental principle in quantum mechanics that states that it is impossible to simultaneously know the exact position and velocity of a subatomic particle.
The Uncertainty Principle states that the more precisely we know the position of a particle, the less precisely we can know its velocity, and vice versa. This is due to the wave-particle duality of subatomic particles, where they exhibit both wave-like and particle-like behavior.
The Uncertainty Principle places a limit on the precision of measurements that can be made in quantum mechanics. This means that there is always a degree of uncertainty in any measurement of a subatomic particle's position and velocity.
No, the Uncertainty Principle is a fundamental principle in quantum mechanics and cannot be violated or circumvented. It is a consequence of the probabilistic nature of subatomic particles and is supported by numerous experimental observations.
The Uncertainty Principle also applies to energy, stating that the more precisely we know the energy of a particle, the less precisely we can know the duration of its existence. This is known as the energy-time uncertainty principle and has important implications in the study of unstable particles and nuclear reactions.