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 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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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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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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1answer
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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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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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1answer
125 views

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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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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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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1answer
209 views

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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1answer
49 views

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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1answer
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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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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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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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1answer
350 views

Why do we need virtual particles?

I understand the $\Delta t \cdot \Delta E \geq \hbar / 2$ relationship and the idea behind them. However, I don't understand why do we need them at all. I'm a physics undergraduate. As far as I know, ...
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1answer
43 views

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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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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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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2answers
150 views

Minimum uncertainity

I'm confused in finding the condition for minimum uncertainty, The author in the book I refer goes on saying that $|g\rangle=c|f\rangle$ is the condition for minimum uncertainity for some constant ...
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1answer
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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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1answer
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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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91 views

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 ...
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151 views

Relation between $\Delta E$ and $\Delta p$

This will be a very quick question. I've seen in some books, that when describing the Heisenberg uncertainty principle, it was used implicitly the application of the following statement: $$\Delta ...
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1answer
71 views

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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2answers
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Does the uncertainty principle imply the existence of particles that exceed the speed of light?

The uncertainty principle allows for the creation of virtual particles (with non-zero mass) that exist for very short durations. This allows empty space to have particle pairs that pop into existence ...
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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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Underlying C*Algebra operators in standard quantum mechanics?

Linearity in standard quantum mechanics (QM) is the key to making the math possible in this field, but the presence of nonlinear operators in QM is what is more generally dealt with. Working with the ...
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In the double slit experiment with electrons why the single slit case is not diffracting as photons would have?

The famous double slit experiment used in books to describe the duality of particles nature usually presents a case where only one slit is open and there is no diffraction. Aren't we supposed to see ...
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How can I calculate the uncertainty in radioactive decay

So I have an exercise that says that the initial rate of $14\mathrm{C}$ was $13.5$ (per second) and nowadays it $10.8$ (per second). The half-life time is $5730$ years with an uncertainty of $30$ ...
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1answer
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A Confusion About Energy-Time Uncertainty Relations

In all the textbooks that I have seen, energy-time relation is written in the following way:$$\Delta E \cdot \Delta t \geqslant \frac{\hbar}{2}$$ Here is my interpretation of this principle: The ...
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1answer
94 views

Calculating energy eigenvalues when potential is given

So our teacher claimed that if we have a Potential of the form $V(x)= x^\nu$ then the Energy is of the form $E={2\nu \over \nu+2}$ Can anyone break up the math for this problem?
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Is quantum physics truly random or does it just appear that way because of Heisenberg uncertainty principle

The behavior of an electron (and other tiny things) is said to be probabilistic because we can't say where an election will be when we measure it, but only where it will probably be. As I understand ...
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1answer
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The uncertainty in angular momentum

It is known that the different spatial components of the angular momentum don't commute with each other. $$ [L_x,L_y] \propto L_z \\ [L_y,L_z] \propto L_x \\ [L_z,L_x] \propto L_y $$ Also it is known ...
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Uncertainity principle and double slit experiment?

My Understanding of uncertainty principle goes that if some particles are in same state, then their measurement of certain property (say $x$ and $p$) will be different for different particles. ...
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1answer
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Does the uncertainity principle actually attack determinism? [closed]

It's not really clear to me how does QM attacks determinism. It sure attacks computability, which is a component of newtonian, naive determinism, but it's often claimed to destroy determinism itself ...
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1answer
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Do Quantum Mechanics At The Macro Scale Disprove General Relativity or Prove Something New?

We all know about the discrepancy between relativity and quantum physics at the scale relative to particles. Wouldn't the fact that recent experiments show quantum effects at the macro-scale in some ...
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2answers
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Why can't be the EPR experiment simplified?

Alice measures the spin of her electron on the x axis. She now knows the spin value of Bob's electron on the x axis at time T0. Bob measures the spin of his electron on the z axis. He now knows the ...
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1answer
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When to use different forms of the similar looking uncertainity equations?

I usually find two different forms of Heisenberg's uncertainty principle equations as in follows: $$ \Delta x \cdot \Delta p \ge h$$ $$ \Delta x \cdot \Delta p \ge (\frac{h}{2\pi})$$ Some text ...
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Can a buckyball gun be fired by observing it?

If a buckyball was placed inside a gun made from maybe a carbon nanotube or something, would measuring the momentum of the buckyball cause the the gun to fire? At what speed would the buckyball exit ...
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Zero-point energy amplitude calculation

On this page https://www.miniphysics.com/simple-harmonic-oscillator.html It is stated that for a linear restoring force of $F = -k \Delta x$, the total energy is $ E = K + U $ or rather $ \\ E = ...
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1answer
110 views

Retarded Quantum Harmonic Oscillator

Suppose there is a harmonic oscillator and at some time acts on him a force. The external force $F (t)$ being zero before $t = 0$ and after $t = T$ . The oscillator was in its ground state for all ...
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Doesn't Uncertainty Principle disproves the whole Quantum Physics's measurements?

Let's say Heisenberg was right that we can't measure both location and velocity of a small particle at the same time, So doesn't it say that the observations of any experiment that we have done in all ...
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298 views

'The size of an atom' using Uncertainty Principle

Suppose we have a hydrogen atom, and measure the position of the electron; we must not be able to predict exactly where the electron will be, or the momentum spread will then turn out to be ...