# Heisenberg Uncertainty Principle problem

• K.QMUL
In summary, the Heisenberg Uncertainty Principle states that in quantum physics, the standard deviations of position and momentum cannot both be zero at the same time. This is due to the fact that as one decreases, the other must increase in order to maintain a minimum product of h-bar/2. However, in classical physics, the momentum and position of an object can both be zero. This shows how classical physics is a limit of quantum physics when h-bar tends to 0.
K.QMUL

## Homework Statement

Explain, using the Heisenberg Uncertainty Principle, how classical physics is reached a a limit of quantum physics when (h-bar) tends to 0.

## Homework Equations

ΔxΔp(x) ≥ (h-bar)/2

## The Attempt at a Solution

The only reasonable answer I can formulate is the fact that when 'h-bar' is zero, the momentum/its kinetic energy is greater than or equal to zero. However in classical physics the kinetic energy of an object can be zero (if its at rest), whereas in Quantum physics, using the Heisenberg Uncertainty principle above, it cannot be zero.

Any help?

Last edited:
You're almost there. Take note that the delta-x and delta-p in the uncertainty relation are not the position and the momentum of the particle, but the standard derivations of them, which measure the "uncertainty" of each variable.

Therefore if the right-hand-side is 0 there is actually no restriction on them, as the relation would only state that their product must be positive and that is always true (they are both always positive).

If the bar-h is not cero, though, we run into problems. Imagine you have a "fixed" delta-x and a delta-p that decreases over time (because we perform better experiments, for example). The product on the left-hand-side will decrease as well, and eventually it will be equal to the right-hand-side, so that another decreasing would "break" the rule, it would make it lower. According to the Uncertainty Principle one of two things should then occur: either delta-p would stop decreasing (we could not do a better experiment) or either delta-x would start increasing (experiments would show more accurate p measures but less acurate x measures).

I hope this helps.

Thanks, that does help! But is my explanation complete if I consider it to be standard deviations? Is there anything else I am missing to explain?

K.QMUL said:
Thanks, that does help! But is my explanation complete if I consider it to be standard deviations? Is there anything else I am missing to explain?

Mmm, not quite. You say that in quantum mechanics momentum can't be zero. I don't see why neither momentum or its standard derivation could not be zero.

Let me put the relation on words: if delta-p or delta-x decrease the other one must increase (or viceversa) so that their product is always a minimum (namely h-bar/2). If that minimum is satisfied (because it is really little or even zero) they can take pretty much any value.

Right, sorry, I forgot to put that in. I did write that down previously however. Thanks!

## 1. What is the Heisenberg Uncertainty Principle?

The Heisenberg Uncertainty Principle is a fundamental concept in quantum mechanics that states that it is impossible to simultaneously know the exact position and momentum of a particle. This means that the more accurately we know the position of a particle, the less we can know about its momentum, and vice versa.

## 2. Who discovered the Heisenberg Uncertainty Principle?

The Heisenberg Uncertainty Principle was first proposed by German physicist Werner Heisenberg in 1927 as part of his uncertainty principle theory. Heisenberg's work revolutionized the field of quantum mechanics and earned him the Nobel Prize in Physics in 1932.

## 3. How does the Heisenberg Uncertainty Principle impact measurements in quantum mechanics?

The Heisenberg Uncertainty Principle sets a limit on the accuracy of measurements in quantum mechanics. It means that there will always be a degree of uncertainty in the measurements of position and momentum of a particle, no matter how advanced our technology becomes.

## 4. Can the Heisenberg Uncertainty Principle be violated?

No, the Heisenberg Uncertainty Principle is a fundamental law of quantum mechanics and cannot be violated. It is not a limitation of our technology or measurement methods, but rather a fundamental aspect of the behavior of particles at the quantum level.

## 5. How does the Heisenberg Uncertainty Principle relate to the concept of wave-particle duality?

The Heisenberg Uncertainty Principle is closely related to the concept of wave-particle duality, which states that particles can exhibit both wave-like and particle-like behavior. The uncertainty principle is a manifestation of the wave-like nature of particles, as it is impossible to precisely measure the position of a particle due to its wave-like nature.

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