# Questions tagged [heisenberg-uncertainty-principle]

This tag is for Heisenberg's quantum mechanical uncertainty principle. DO NOT USE THIS TAG for uncertainty in a non-quantum measurement.

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### How does the uncertainity principle apply in this situation?

A common (but, as I think, incomplete) description of the uncertainity principle is the following: You cannot determine a particle's momentum and position at high accuracy at the same time It could ...
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### Probability question based on Heisenberg's uncertainty principle?

Heisenberg's uncertainty principle relates energy and life time $\tau$ of a particle as follow: $\tau=\frac{\bar{h}}{1+x^2}$ Here energy is approximated as $1+x^2$ where $x$, the velocity of particle, ...
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### Can we think about a particle trapped in a potential well in terms of “quantum measurement”?

Usually, when I'm thinking about a quantum measurement, I see a sort of particle that is being hit by a photon. The more energy the photon carries, the more the momentum of the particle is disturbed, ...
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### Is the Uncertainty Principle a mathematical consequence or a physical consequence or both? [duplicate]

I am currently exploring the mathematical structure of Quantum Mechanics on an introductory level. A couple of books and online sources (including this website) stated how the Uncertainty Principle is ...
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### How is the uncertainty principle related to the non-commutativity of the multiplication of operators in quantum mechanics? [duplicate]

The way I understand the uncertainty principle is that it's not even really about quantum mechanics specifically -- it's just a property of waves. e.g. A periodic wave doesn't even have a well ...
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### What's the relationship between the definition of the uncertainty principle using standard deviations vs using $\Delta x$ and $\Delta p$?

So I've heard two different explanations of the uncertainty principle, both of which make sense on their own, but I'm having a hard time figuring out how they're connected. The first is that the ...
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### Why cant we lower temperature to X where if an electron is observed it will be as if its an unobserved Temperate Y

Lets say the temperature is Y, and we want to observe an electron but if we do we will use a high energy light wave which will make it act more like a particle, so why dont we just lower the ...
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### What does the uncertainty principle tell us about the harmonic oscillator?

For the harmonic oscillator we have $\sigma_x \sigma_p = \hbar(n+1/2)$ and by the uncertainty principle $\sigma_x \sigma_p \geq \frac{\hbar}{2}$. In one of the exercises I was doing I was asked to ...
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### Deriving a uncertainty inequality

Starting from $$(Δx) (Δp) \geq h/2$$ How does one derive $$a^2 (Δx)^2 + (Δp)^2 \geq a h~?$$
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### How can infinite sine waves localize to a single pulse in space?

I have heard countless times (and not just when discussing the Heisenberg's Uncertainty Principle) that making a short pulse using sine waves requires more and more sine waves to localize the pulse ...
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### Different definitions of the uncertainty principle

In the book Introduction to Quantum Mechanics by Griffiths, the mathematical form of the uncertainty principle is stated as $$\sigma_x \sigma_p \ge \frac{\hbar}{2}.$$ However, another book on QM, that ...
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### If particles like the $W$ boson can have a range of masses, can quarks and leptons also have a range of masses?

The reason why the weak nuclear force is weak is because the mediators, the $W$ and $Z$ bosons, need to take on a ridiculously high mass compared to the mass that they are usually found at (which is ...
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### Trying to prove Heisenberg's uncertainty wrong [duplicate]

Heisenberg’s uncertainty principle states that we cannot determine the position and momentum of a particle at a time. I think I have an idea to prove it wrong ( although I believe I must be wrong here)...
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### Complete set of commutating obsevables and Uncertainity Relation

In quantum mechanics, I read that when operators corresponding to observable commute, then they form a complete set that can define the state of the system. But in the case of $1$ dimension, we say ...