# 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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### The uncertainty principle and two-particle collisions

It is not possible to simultaneously know the exact position and momentum of a particle as a consequence of non-commutativity of the position and momentum operators. But what if I consider a simple ...
54 views

### The Fisher information in QM

What is the relationship of the minimum Fisher information, Fourier transformation and position-momentum uncertainty relation in QM? To what degree these concepts revolve around the same thing?
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### Different forms of Heisenberg Uncertainty Principle

The Heisenberg Uncertainty Principle is often written in two forms: $$\Delta x \Delta p \geq \frac{\hbar}{2}$$ and $$\sigma_x \sigma_p \geq \frac{\hbar}{2}.$$ Are these two equivalent? I've been ...
143 views

### Uncertainty relation in mixed states

If a system is in a pure state $|\psi\rangle\langle\psi|$ we have $$\sigma_A\sigma_B\geq\frac{1}{2}|\langle[A,B]\rangle|.$$ Generalize this and find an uncertainty relation for an arbitrary mixed ...
4k views

### How do I interpret uncertainty in velocity greater than the speed of light?

I just studied Heisenberg's uncertainty principle in school and I came up with an interesting problem. Assume an electron which is moving very slowly and we observe it with a distance uncertainty of ...
116 views

### What is the maximum number of bounces a ball can be expected to make on another fixed ball of same radius on the ground?

In the book 'Quantum Mechanics' by Leonard I. Schiff, this question can be found at the end of chapter one. More specifically it asks: A perfectly elastic ping pong ball is dropped in vacuum from a ...
443 views

### Trapping an electron

Imagine that one could theoretically trap a single electron in a small box, with walls that somehow prevent the electron from passing through and out of the box. Now, the box begins to move in on ...
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### How uncertainty principle can be used to calculate the range of actual variables

I know the uncertainty relation $\Delta x \Delta p \ge \frac{\hbar}{2}$ tells the uncertainty in position and momentum, or energy and time should be greater than or equal to $\frac{\hbar}{2}$, but I ...
177 views

### Feynman's path integral and uncertainty principle?

The Feynman's path integral representation gives the quantum amplitude to go from point $x$ to point $y$ as an integral over all paths. How is that idea consistent with the uncertainty principle that ...
138 views

### Uncertainty as a founding principle of QM? [closed]

Ideally, every new physical theory is derived from its fundamental principles. Hall & Reginatto derived the Schrödinger equation from an uncertainty principle and probabilistic classical mechanics,...
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### Looking for a simplified explanation for why you cannot measure velocity and pin point location

Because of uncertainty, you cannot measure both velocity and exact position. Is this because when you measure the position of a particle, it is freezing it in its frame of reference? When measuring ...
149 views

### Is it true that we can't measure position and momentum together?

The uncertainty principle states that there always will be mean variance if we measure position or momentum. It does not state that the measurement is wrong. It only states that there always will be a ...
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### Position and momentum of an electron in a hydrogen atom [closed]

What can be expected as results for a set of position and momentum measurements of an electron in a hydrogen atom? I believe that for the position, we can expect something depending on the radial ...