# Tag Info

## New answers tagged heisenberg-uncertainty-principle

### Extension of uncertainty principle to mixed-states

Consider the variance of an observable $A$ with respect to a generic mixed state $\rho$: $$\operatorname{Var}[A|\rho] \equiv \operatorname{tr}(\rho A^2)-\operatorname{tr}(\rho A)^2,$$ also written ...
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1 vote

### If momentum is a function of position, then how does the uncertainty principle work?

There are no trajectories in quantum mechanics. In classical mechanics, you can talk about the position of a particle as a function of time, $x(t)$. Then, from there, you can derive the momentum as a ...
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1 vote

### If momentum is a function of position, then how does the uncertainty principle work?

In classical physics the position of a particle is described at a a given time by a set of numbers $(x(t),y(t),z(t))$. If you were to measure the $x$ position of a particle at time $t$ you would get ...
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### If momentum is a function of position, then how does the uncertainty principle work?

Velocity, like any quantity in quantum mechanics, is an operator. We can obtain its form using the standard prescription for obtaining the "operator of time derivative":  \hat{v}=\hat{\dot{...
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### If momentum is a function of position, then how does the uncertainty principle work?

If I understand correctly, Heisenberg's Uncertainty Principle holds that position and momentum cannot be known with absolute precision simultaneously. That is the consequence of the principle, but it ...
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### Wrong explanation for why "electron can't exist in the nucleus"?

Electrons do "spend time" inside the nucleus, just as they "spend time" in other spherical regions of a similar size. You can see that from the fact that the $1s$ orbital wave ...
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### Wrong explanation for why "electron can't exist in the nucleus"?

Everything @BioPhysicist is correct, but in addition: Your argument is semi-classical, quantum mechanics is non-relativistic (there is no $c$ in the Schrödinger Eq.), and the problem involves ...
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### Wrong explanation for why "electron can't exist in the nucleus"?

When are asked about why an electron cannot fall into the nucleus... This is a common "problem" when talking about the issues with the classical picture of an electron orbiting the nucleus, ...
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1 vote
Accepted

### Uncertainty principle probability

With the uncertainty principle in quantum mechanics, there is indeed an inherent trade-off between the precision of the position and momentum measurements of a particle. However, it is not a simple ...
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### Does Heisenberg's Uncertainty principle Imply the universe is finite/periodic?

If you are confined to a finite interval of space where your wave function must be $0$ outside the interval, then there are discrete solutions to the Schrodinger equation. For the simple case of a ...
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1 vote

### Does Heisenberg's Uncertainty principle Imply the universe is finite/periodic?

That is to say, if there's a limit of the form "you can't have infinite velocity" then there are are only a finite number of harmonics implying a finite/periodic universe. Relativity says ...
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### Are there any theoretical reasons why we cannot measure the position of a particle with zero error?

You might try a thought experiment: how can I measure the position of a particle with minimal (ideally zero) error? This is how my sixth form physics teacher introduced Heisenberg's uncertainty ...
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### Are there any theoretical reasons why we cannot measure the position of a particle with zero error?

Continuous variables can't be measured with zero error in principle, already due to them being real numbers, nothing to do with quantum theory. It would take infinite number of digits to write down ...
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### Are there any theoretical reasons why we cannot measure the position of a particle with zero error?

The Planck length is hypothesised as the minimal length measurement, so we shouldn't expect to measure the position of an electron with uncertainty much smaller than this value.
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### Are there any theoretical reasons why we cannot measure the position of a particle with zero error?

In quantum mechanics the two variables (i) position x and (ii) momentum are "correlated" in the sense that if we multiply their uncertainties, they have to exceed a certain number. This is ...
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