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Joker93
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I have read that the Schrodinger Uncertainty Principle is an extension of Heisenberg's. So, why don't we use the Schrodinger Uncertainty Principle instead of Heisenberg's?
Thanks!
Thanks!
Which one is that?Adam Landos said:Schrodinger Uncertainty Principle
https://en.wikipedia.org/wiki/Uncer...2.80.93Schr.C3.B6dinger_uncertainty_relationsblue_leaf77 said:Which one is that?
Which one do researchers use?dextercioby said:The only reasonable answer to the posed question is that:
1. Textbook writers are traditionalist.
2. Robertson's formulation is simpler, thus better suitable for a textbook written for a greater audience.
oh, ok. So, this also affects [x,p]=ihbar?dextercioby said:I wouln't know, I ain't one. But this is well-established physics since 1929 anyway.
Most of the time: none. The uncertainty principle alone is rarely sufficient to determine what happens, and if you use the more powerful tools of quantum mechanics the uncertainty principle is satisfied automatically.Adam Landos said:Which one do researchers use?
That's a fundamental commutation relation, so it will not change. In fact this relation affects the particular form of the uncertainty relation involving position and momentum.Adam Landos said:this also affects [x,p]=ihbar?
I think it's just a matter of convenience. The general form of the uncertainty principle is like ##(\Delta A \Delta B)^2 \geq C_1 + C_2## where ##C_1## and ##C_2## are real, positive numbers. Now, these two unequalities are true ##(\Delta A \Delta B)^2 \geq C_1## and ##(\Delta A \Delta B)^2 \geq C_2##. Most people, however, choose to use the commutator as the minimum value because I think in most cases, it has special simple form for a given pair of noncommuting observables.Adam Landos said:I have read that the Schrodinger Uncertainty Principle is an extension of Heisenberg's. So, why don't we use the Schrodinger Uncertainty Principle instead of Heisenberg's?
Thanks!
So, does it affect Δx*Δp>=hbar/2?blue_leaf77 said:That's a fundamental commutation relation, so it will not change. In fact this relation affects the particular form of the uncertainty relation involving position and momentum.
In your question, what affects what?Adam Landos said:So, does it affect Δx*Δp>=hbar/2?
We get that inequality for the product of the uncertainty of the momentum and position from the standard inequality(Heisenberg's inequality). Is it more correct to use the other inequality?blue_leaf77 said:In your question, what affects what?
The other inequality, which is more general, was derived without omitting anything (or at least it omits less frequent than the simpler Heisenberg inequality). This means, the general uncertainty principle is always automatically satisfied for any state. Since it is always satisfied, getting rid of one the terms in the lower bound of the inequality will not affect its validity.Adam Landos said:Is it more correct to use the other inequality?
So, why even consider using the more general inequality if the standard inequality gives a lower bound?blue_leaf77 said:The other inequality, which is more general, was derived without omitting anything (or at least it omits less frequent than the simpler Heisenberg inequality). This means, the general uncertainty principle is always automatically satisfied for any state. Since it is always satisfied, getting rid of one the terms in the lower bound of the inequality will not affect its validity.
Which one are you terming as "general", the Schroedinger's or Heisenberg's uncertainty?Adam Landos said:general inequality
Adam Landos said:So, why even consider using the more general inequality if the standard inequality gives a lower bound?
I think the more general is Schroedinger's. I am referring to Heisenberg's as the standard one! :Dblue_leaf77 said:Which one are you terming as "general", the Schroedinger's or Heisenberg's uncertainty?
The Schrodinger Uncertainty Principle is important because it is a fundamental principle in quantum mechanics that describes the inherent uncertainty in the measurement of certain physical properties of particles. It shows that there are limits to the precision with which we can measure certain pairs of properties, such as position and momentum.
The Schrodinger Uncertainty Principle challenges our classical understanding of the physical world by showing that at the quantum level, particles do not have definite properties until they are observed. This means that our ability to predict and control the behavior of particles is limited by the inherent uncertainty in their properties.
The Schrodinger Uncertainty Principle only applies to particles at the quantum level and is not noticeable in our everyday lives. The uncertainty in the measurement of properties is so small that it is only relevant in the microscopic world of atoms and subatomic particles.
No, the Schrodinger Uncertainty Principle is not a barrier to scientific progress. In fact, it has been instrumental in the development of quantum mechanics and has led to important discoveries and advancements in technology, such as transistors and lasers.
No, the Schrodinger Uncertainty Principle is a fundamental law of quantum mechanics and cannot be violated. It is a mathematical expression of the inherent uncertainty in the measurement of certain properties of particles and has been experimentally confirmed countless times.