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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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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4answers
852 views

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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95 views

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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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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154 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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2answers
145 views

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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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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1answer
157 views

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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1answer
93 views

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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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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Proof of Canonical Commutation Relation (CCR)

I am not sure how $QP-PQ =i\hbar$ where $P$ represent momentum and $Q$ represent position. $Q$ and $P$ are matrices. The question would be, how can $Q$ and $P$ be formulated as a matrix? Also, what is ...
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1answer
95 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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2answers
262 views

Is there any physical quantity that does not have uncertainty?

I saw this video and I got a thought: Is there any physical quantity that does not have uncertainty? Basic models are: for lenght for time end energy (so for mass too) and I realized that ...
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1answer
386 views

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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3D Minimum uncertainty wavepackets

Based on the 1D case mentioned in Griffiths, I decided to try looking at the features of 3D Gaussian wavefunctions, i.e. (position basis) wavefunctions of the form $\psi(\mathbf{r}) = ...
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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
83 views

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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Why is the Heisenberg uncertainty principle stated the way it is?

I spent a long time being confused by the Heisenberg uncertainty principle in my quantum chemistry class. It is frequently stated that the "position and momentum of a particle cannot be ...
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'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 ...
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1answer
117 views

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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246 views

Why does temperature have no uncertainity?

Background My understanding is that temperature is not a quantum mechanical operator. Hence, thereby it should not have any uncertainty. However, any instrument that tries to take the measurement of ...
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1answer
254 views

Which position and momentum distributions arise from some wave function?

Consider a particle in one dimension with wave function $\psi(x)$. The probability density function describing how likely it is to find it in a given position is given by ...
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1answer
46 views

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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35 views

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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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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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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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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1answer
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Heisenbergs Uncertainty Principle in different intertial frames

Say there is a single particle in a box. If we switch to a different inertial frame (without the box) travelling close to the speed of light we see the box get smaller. At a high enough speed the ...
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Is uncertainity a postulate? [duplicate]

I heard the standard interpretation of Heisenberg Uncertainty Principle: Just the measurement affects the position of the body because always you want to see a body (=to measure the position), you ...
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2answers
131 views

Is there a mathematical relationship between Legendre conjugates and Fourier conjugates?

In quantum mechanics, there is an uncertainty principle between conjugate variables, giving rise to complementary descriptions of a quantum system. But the variables are conjugates in two different ...
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1answer
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Why isn't it possible to determine a particle's position without changing its velocity

So, I think understand the premise of the Heisenberg uncertainty principle, but it seems to me that someone would be able to create a device which would be able to measure the position of a particle ...
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Two questions about Feynman propagator

Taking for example the meson propagator: $$ \Delta_F (x-y) = \int \frac{d^4k}{(2\pi)^4} \frac{e^{-ik(x-y)}}{k^2 - m^2 + i\epsilon}. $$ It describes a meson that propagate from a point of Minkowski ...
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Uncertainty principle on a simple pendulum

During simple pendulum motion at different points it has specific energy.That is how we can precisely predict its velocity as well as its definite position. It seems to violate Heisenberg's ...
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356 views

Is the uncertainty principle a statement about limits on our predictive rather than our measurement abilities?

Here's what I know. The Uncertainty Principle states that $$\sigma_x \cdot \sigma_p \geq {{\hbar} \over 2}$$ However, I also know that this principle refers to measurements performed over many ...
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How Uncertainty Principle, Vacuum fluctuations and Energy Conservation coexist in QFT?

Recently I had a debate about the uncertainty principle in QFT that made me even more confused.. Because we use Fourier transforms in QFT, we should have an analogue to the usual Heisenberg ...
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1answer
113 views

How relevant is the Heisenberg Uncertainty Principle?

I was originally surprised to see that, $$\Delta x \cdot \Delta p \gt {{\hbar} \over 2}$$ But, then I realized that $\hbar/2=5.27 \cdot 10^{-35}$. According to this other question, the smallest ...
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1answer
94 views

Is the Uncertainty Principle a logical consequence from the Wave-Particle duality?

I always thought of the Uncertainty Principle as a logical consequence that follows from the Wave-Particle duality, or more precise, from the fact that all particles behave as waves as long as they do ...
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1answer
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“Derivation” of the Heisenberg Uncertainty Principle

The question I outline below is my textbook's "derivation" of the Heisenberg Uncertainty Principle. The "derivation" my textbook uses involves wave packets. Suppose there are seven waves of ...
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2answers
166 views

Why is Heisenberg uncertainty principle not valid in waves in string?

We know from high school physics that when the incident wave is traveling from a low density region (high wave speed) region towards a high density (low wave speed) region on a string, the width of ...
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1answer
96 views

Is there uncertainity of position of the perfectly homogenous radiating body?

I heard the standard interpretation of Heisenberg Uncertainty Principle: Just the measurement affects the position of the body because always you want to see a body (=to measure the position), you ...
0
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1answer
59 views

Can the uncertainty principle be redefined for different standard deviations?

$$\sigma_x \cdot \sigma_p \ge {{\hbar} \over {2}}$$ Where the $\sigma$ is the standard deviation. What happens to the inequality if you use a different definition of $\sigma$. For instance what ...
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How can Particle Accelerators even crash particles?

In quantum mechanics there is a law that states we cannot know a position and the momentum of a particle and so in a particle accelerator, we need to know the position of the particles we are going to ...
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Derivation of minimum uncertainty from Squeezed Coherent State [closed]

I'm studying a book in which I stopped by this point. I don't know how to derive the inequality from $$tr(\rho A^{*}A )?$$
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Can we theoretically balance a perfectly symmetrical pencil on its one-atom tip?

I was asked by an undergrad student about this question. I think if we were to take away air molecules around the pencil and cool it to absolute zero, that pencil would theoretically balance. Am I ...
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Does Digital Physics imply Heisenberg's Uncertainty Principle? [closed]

I made the following observation which led me to believe that perhaps Digital Physics implies Heisenberg's Uncertainty Principle: Consider Noether's Theorem, which states that space-translation ...