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 do we know that there is a wavefunction which collapse?

How do we know that there actually is a wavefunction in the first place which collapse. How do we know that there is a transition from some linear combination of the eigenfunctions to a single one? ...
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How to estimate the ground state of a potential well when a confinement dimension is added

I have a finite harmonic potential where I trap an electron. The confinement length changes in size. Now, I'm interested in the ground state energy, so I have this 1D Poisson solver which gives me the ...
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Distinguish statistical uncertaincy from noise disturbance relation in slit gedankenexperiment

I am just reading the "Statistical Interpretation of Quantum Mechanics" from L. Ballentine. In section 3.2. he discusses the difference between the observer effect and the statistical ...
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3answers
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Decrease of uncertainty of momentum with increase of width of infinite well in QM(intuition)

Why does the uncertainty in the momentum decrease with the increase of the width for an energy eigenstate in the classic problem if the infinite well in Quantum Mechanics? I have worked out the ...
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Application of uncertainty principle [duplicate]

why doesn't Heisenberg's uncertainty principle also work for macroscopic bodies which are in-turn made up of quantum-particles? ps: if proof is provided it will be a lot more useful.
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1answer
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Finding natural linewidth's

I want to check whether my fit parameter for the width of a Lorentzian fit on my digital spectroscopy data for Helium (the 5875 Angstrom line) is what you would expect from the uncertainty principle, ...
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Reason behind the uncertainty principle [duplicate]

I know that Heisenberg Uncertainty principles states that the momentum and position of a quantum object can not be determined at the same time. This is very strange to me. I want the basic reason ...
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Heisenberg Uncertainty Principle scientific proof

Heisenberg's uncertainty principle states that: $$\sigma(x)\sigma( p_x )\ge \frac {\hbar}{2}.$$ What is the scientific proof of this principle? Operators Uncertainty
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Reason for Uncertainty principle

$$\Delta x \Delta p_x \geq \frac{\hbar}{2} $$ I understand what does Heisenberg's uncertainty principle states i.e. it's definition and it has been proven experimentally. But, can anyone please ...
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Is there something behind non-commuting observables?

Consider a quantum system described by the Hilbert space $\mathcal{H}$ and consider $A,B\in \mathcal{L}(\mathcal{H},\mathcal{H})$ to be observables. If those observables do not commute there's no ...
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Quantum Theory just lazy physics?

Is it true that physicists decided that because they couldn't predict with certainty the location of an electron at any given time, that they just created equations using probability instead, still ...
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96 views

Relationship between Quantum superposition and Uncertainty principle

I'm an amateur in quantum mechanics. I am confused after reading the following in the wikipedia article about quantum superposition: If the operators corresponding to two observables do not ...
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Why doesn't $σ_xσ_p$ change with the width of the well in the infinite square well problem (intuition)?

I calculated that the product of the uncertainty in position $\sigma_x$ for the ground state of an infinite square well of width $L$ with the uncertainty in the momentum $\sigma_p$ for the same state, ...
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1answer
92 views

Is there a simple way to explain quantised conductance? [closed]

I am biologist and I need to pass a nanotechnology class. I am stuck with this term of quantum resistance. Basically this appears to me as normal Ohm's law, except that takes into account Heisenberg ...
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3answers
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Would the uncertainty principle apply to gravitational waves?

The uncertainty principle is one of the most basic rules of quantum mechanics, but Quantum mechanics still has not been unified with general relativity, so would the uncertainty principle apply to ...
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1answer
110 views

What does it mean that an electron's position is described by probability?

I just read an answer to a Phys.SE question about why electrons don't collide with protons where an answering user said: In quantum mechanics, an electron doesn't have a definite position or ...
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Heisenberg Uncertainty Principle: Which formula is correct?

Some websites and textbooks refer to $\Delta x \Delta p \geq \frac{\hbar}{2}$ as the correct formula for the uncertainty principle whereas other sources use the formula $\Delta x \Delta p \geq \hbar$ ...
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2answers
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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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3answers
243 views

Uncertainty principle and multiple observers

My understanding is that an observer can measure the precise location of a particle so long as the corresponding uncertainty in momentum measurement is not an issue and vice-versa. Say there is ...
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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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1answer
92 views

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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1answer
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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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1answer
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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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16answers
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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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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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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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3answers
267 views

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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1answer
139 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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2answers
218 views

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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2answers
71 views

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 ...