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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Does Heisenberg's Uncertainty Principle describe real uncertainty or measured uncertainty?

Some derivations of Hesenberg's Uncertainty principle are based on the momentum of light or particles used in measuring an object's position and momentum. Does this lower limit on uncertainty describe ...
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Momentum and position for free particle

In the section of 'The free particle' in 'Introduction to quantum mechanics, second edition' by Griffiths page 65. He has the wave equation as $$\Psi(x,t) = \frac{1}{\sqrt{2 \pi}} ...
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What does it mean “not to have a definite trajectory”?

In a comment to my question someone stated the following: "photons do not travel at some definite number of oscillations per second. In fact, they do not "travel" at all, no more than electrons ...
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What is the Quantum Mechanical Operator for Electric Potential?

I understand that charge and electric potential are conjugate observables in QM. See https://en.wikipedia.org/wiki/Conjugate_variables The quantum mechanical operator for charge, q, is simply equal ...
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Heisenberg Uncertainty Relation and Relativity

It's well known that in QM the position and momentum of a particle cannot be known simultaneously. It's also well known that in special relativity the idea of simultaneity loses its meaning. Would it ...
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Is the momentum of a microscopic particle always equal to or less than the error of momentum

In class we tried to show that the electron can't reside inside the nucleus using uncertainty principle . We took the radius of nucleus as error in positon and found the error in momentum. The teacher ...
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A quantum particle which is almost at rest but whose position is random!

Assume a particle is given by a quantum state which is constructed in such a way that it is equally probable to find it anywhere in an fixed interval $(0,L)$ but has arbitrarily low velocity. The ...
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The link between non-locality and Heisenberg's uncertainty relations

I have recently found out1 that the concepts of non-locality and Heisenberg's uncertainty do not live independently of one another in Quantum Mechanics. In other words, roughly the idea goes as: the ...
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How can I solve this quantum mechanical “paradox”?

Let a (free) particle move in $[0,a]$ with cyclic boundary condition $\psi(0)=\psi(a)$. The solution of the Schrödinger-equation can be put in the form of a plane wave. In this state the standard ...
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How is the motion of electron in p orbital?

Does an electron in p orbital move around nucleus or move randomly in any individual lobe of p orbital. if it were to move around nucleus then does p orbital move along with it?
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Does the uncertainty principle go against chaos theory?

My understanding of the uncertainty principle and quantum physics is that any given object may, without notice or explanation, spontaneously perform an action it previously was unable to do with a ...
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When uncertainty is calculated in non normalized eigenstates it doesn't give zero. Shouldn't it give zero?

Suppose $\Psi$ is an eigenstate of observable $\text H$ with eigenvalue $E_1$. Then uncertainty in the value of $\text H$,$(\Delta E)^2=\langle E^2\rangle-\langle E\rangle^2$ which gives,$(\Delta ...
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Apparent paradox concerning Heisenberg's uncertainty principle

I have just begun my Introduction to Quantum Mechanics course in my undergrad and I am trying to understand the uncertainty principle on a fundamental level. I think the best way to understand the ...
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Can the Heisenberg Uncertainty Principle be explained intuitively?

I have heard several pseudoscientific explanations about the Heisenberg Uncertainty Principle and find them hard to believe. As a mathematician mainly focusing on functional analysis, I have a ...
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NO Uncertainties for particles in their own frames!

Well I had this thought experiment in which a particle observes itself, and something like the following is observed. Taking in mind the uncertainty principle all particles even stopped at 0K jiggle ...
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175 views

Does relativity violate uncertainty principle?

Let us say I sit on an electron. According to me the electron is at rest. Also, I will know the position of the electron accurately as I can take the electron as the origin. So, I know both position ...
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Simultaneous measurement of non-commuting observables without uncertainty

A pair of non-commuting Observables $\hat{X}$ and $\hat{P}$ does not have a common set of eigenfunctions, i.e., it can not be measured simultaneously. Let us for the sake of simplicity assume that ...
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Rigorous Mathematical Proof of the Uncertainty Principle from First Principles

While looking at an intuitive explanation for the Heisenberg Uncertainty Principle (related question below), there was a mention of an axiomatic approach to establishing the uncertainty principle. ...
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How does the uncertainty principle make sense of the fact that momentum for massive particles depends in part on position?

The momentum of an object is in part dependent on the change in position meaning the final position minus the initial position. The equation for momentum is $$p=\frac{m \Delta x}{t\sqrt{1-(\Delta ...
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Heisenberg's uncertainity principle

In the Heisenberg uncertainty principle, $$\Delta x \cdot \Delta p \geq \frac{h}{4\pi}$$ The values of $\Delta x$ and $\Delta p$ are the standard deviations which we get from the probability ...
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Holding an electron

Heisenberg has said that the position and velocity of a small object cannot be known 100% accurate. Now, suppose I take a big metal box within which there is only one electron (somehow). I don't know ...
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How do quantum effects scale to a 4 dimensional being?

I just finished High School a couple of weeks ago (Brazilian schedule) and my grandfather gave me a couple of books on quantum mechanics as a gift. I was reading on Heisenberg's Uncertainty ...
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Uncertainty Relation as obtained in Cohen

It starts considering $$\left|\rho\right\rangle = (Q + i\lambda P)\left|\psi\right\rangle$$ where $\lambda$ is an arbitrary real parameter. Then the norm is obtained: ...
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Heisenberg uncertainty in Bose Einstein condensate

What happens to the Heisenberg uncertainty principle, when a system reaches the Bose-Einstein condensed state? In our statistical mechanics lecture, we derived the following formula for the fraction ...
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Problem about proving the uncertainty principle

$f$ and $g$ are two quadratially integrable functions. It is shown from Schwarz inequality, def of variance and an identity of complex numbers that $$(\Delta A)^2(\Delta B)^2=\langle f|f\rangle ...
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Do black holes violate the uncertainty principle?

If black holes have mass but no size, does that imply zero uncertainty in position? If so, what does that imply for uncertainty in momentum?
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How do black holes form without violating the uncertainty principle? [duplicate]

Many videos on YouTube while discussing black holes mention that it's born out of a heavy star when it collapses into a single point and that infinitely curves spacetime around it. When all the mass ...
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Is uncertainty principle due to entropy? [duplicate]

Is uncertainty principle due to entropy or thermodynamics at all , I was wondering
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Simultaneously measurement in quantum mechanics?

In quantum mechanics $A$ and $B$ can be simultaneous measured if mathematically $\hat{A}\hat{B}=\hat{B}\hat{A}$. But how do we actually measure thing simultaneously. $\hat{A}\hat{B}$ is not ...
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Why can you only measure velocity or location in a particle?

I was talking to a family friend in the field of optics at a quantum scale (not sure the proper name for this) and he was explaining to me why you can only determine either the velocity or location of ...
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How is the uncertainty principle protected for a single electron diffraction?

In the experiment where electrons are sent one by one through a slit on a screen behind which there is an electron detector, the electron is said to have a definite position at the time it crosses the ...
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A few questions on wave packets and uncertainty relations

According to Cohen-Tannoudji the wave-function for a one-dimensional free particle can be written as $$ \psi (x,0)=\frac{1}{\sqrt{2 \pi}} \int g(k) e^{ikx} dk.$$ While $g(k)$ is not specified, there ...
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Spacetime and uncertainty principle

I only have limited knowledge of relativity and quantumphysics but as far as I know, the uncertainty principle relates the uncertainty of space and momentum of a particle. Einstein however, explained ...
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The “general uncertainty” of the harmonic oscillator defies the correspondence principle?

If you use the definition of $(\Delta x)^2 = \langle n | x^2 | n \rangle - \langle n | x | n \rangle^2$ and the same for $(\Delta p)^2$ to calculate $\Delta x \Delta p$ for the state $|n\rangle$ of a ...
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Application of Heisenberg's uncertainty principle on photons

While I was hobby-reading about quantum mechanics I came across Heisenberg's theory. But while I was trying to understand it I thought of this: if the speed of light (as well as the momentum of a ...
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Do the position-momentum uncertainty and time-energy uncertainty really exist in QFT?

It is well known from the Quantum Mechanics(QM) that for a particle, there is a position-momentum uncertainty relation: $$\Delta x\cdot \Delta p\geq \frac{1}{2}\hbar,$$ which bascically can be derived ...
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Uncertainty principle clarification

Suppose a mechanical quantum duck is confined in a pond 1m wide. So, what is its uncertainty in position, 0.5m or 1m? As I think, the uncertainty is 0.5m. The reason is that if we choose the middle ...
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Would quantum fluctuations cause problems for scalar-field inflation?

Wheeler once said that spacetime would be highly curved at very small scales because of the uncertainty principle for energy-momentum. In which case the spacetime becomes very bumpy and not smooth ...
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Deriving an equation for the mass of a pendulum (Follow up)?

Following this question: Deriving mass from simple pendulum which is summarized below Some mass $m$ is release from rest at a horizontal position. $m$ reaches the bottom of its path (so directly ...
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What is $\Delta t$ in the time-energy uncertainty principle?

In non-relativistic QM, the $\Delta E$ in the time-energy uncertainty principle is the limiting standard deviation of the set of energy measurements of $n$ identically prepared systems as $n$ goes to ...
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Quantum Fluctuations [duplicate]

Energy is converted to mass and mass to energy. But during quantum fluctuations energy is created without mass, does this not violate the law of conservation of mass and energy?
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Measurement of energy apparently violating the position-momentum Uncertainty Principle in a potential that does not depend on distance?

I am taking a beginning course in QM and I have learnt that the measurement of energy collapses the wavefunction of a particle to one of its energy eigenstates. But some misconceptions regarding this ...
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Non normalisability implies uncertainty principle? [duplicate]

The wave function $\psi(x,t)$ for a free particle assuming that the position and momentum is well defined, can be solved from the schroedinger equation, ...
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Using the uncertainty principle to estimate the ground state energy of hydrogen

I have been reading through this estimate of the ground state energy of hydrogen and others like it. In this one it says it is using the uncertainty principal but then proceeded to use the following: ...
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Can momentum have a complex expectation value?

I'm making examples of wave functions to incorporate in a QM exam. I came up with the following wave function, which gives me some troubles: $$\psi(x,0) = \begin{cases} A(a-x), & -a \leq x \leq ...
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Expectation to uncertainty

We know that in the case of $O$ being an operator, $\langle O^2\rangle-\langle O\rangle^2$ equals to uncertainty as long as $\langle\rangle$ means the mean value (expectation value). if we have $A$ ...
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Does the Heisenberg uncertainty principle hold up for events in the past? [duplicate]

I was watching this youtube video on predicting the future if you can know the exact position and momentum of every particle in the whole universe. But you can't ever know that says Heisenberg. But ...
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1answer
47 views

Range of a mediating particle

My book describes the derivation of the formula $R\approx\hbar/2mc$ by: $$(\Delta E)(\Delta t)\geq\hbar/2$$ The violation of energy conservation is $\Delta E=mc^2$ to create the particle’s mass. Also, ...
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Is the wavelet transform utilized at all in QM?

Excuse any ignorance, but something was on my mind today and my professor didn't give me a very clear answer... Obviously the Fourier Transform is used pretty constantly in QM. What about the wavelet ...
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The nature of the uncertainty principle

I have read different proofs of the uncertainty principle. My questions are: The principle depends on a theory of physics (quantum mechanics). Correct? Given the theory, mathematics is used to come ...