Linked Questions

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Heisenberg Uncertainty principle defined as $\Delta x \Delta p_x \geq h$ versus $\Delta x \Delta p_x \geq \hbar/2$ [duplicate]

At my university, in the during lectures and in the equation sheet for our exams, the formula for the Heisenberg Uncertainty Principle is stated as $\Delta x \Delta p_x \geq h$, for example in one of ...
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414 views

Confusion regarding factor 2 in uncertainty principle [duplicate]

I have encountered a problem regarding Heisenberg's uncertainty principle. Somewhere I found the expression $$\Delta (x) \Delta (p) \geq \hbar$$ Whereas in some other places, $$\Delta (x) \Delta(...
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1answer
523 views

Heisenberg's uncertainty principle - Planck's (reduced) constant divided by $2$ or not? [duplicate]

The most common form of Heisenberg's uncertainty principle I've seen online is $$ \Delta x \Delta p ~\geq~ \dfrac{\hbar}{2}.$$ However, I also regularly see $$\Delta x \Delta p ~\geq~ \hbar. $$ ...
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2answers
576 views

Why is uncertainty $\geq {\hbar}/{2} $ [duplicate]

Almost all uncertainties (for example the position-momentum uncertainty or time-energy uncertainty) are greater than ${\hbar}/{2} $. But what is the derivation of this uncertainty by Heisenberg? Is ...
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0answers
44 views

Different statements of the Heisenberg's uncertainty principle [duplicate]

In different books, but also websites, there are different expressions for the Heisenberg's uncertainty principle. For example, $\Delta x \Delta p \ge h$ (from The Physics of Atoms and Quanta) $\...
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27 views

Explanation of Different factor of $2$ in Formulas for the Uncertainty Principle [duplicate]

I am readind about Heisenberg's Uncertainty Principle and although the main formula most texts use is $$\Delta x\Delta p_{x}\geq \frac{\hbar}{2}$$ or equivalently $$\Delta x\Delta p_{x}\geq \frac{h}...
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1answer
7k views

Application of Heisenberg's uncertainty principle

I've the following application of Heisenberg's uncertainty principle. If a beam of particles in localised in the $x$-direction by a long slit, what is the uncertainty in position? Firstly, I ...
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1answer
694 views

Symbols in Heisenberg's Uncertainty Principle

The uncertainty principle states that $${\Delta}x{\Delta}p{\geq}\frac{h}{4\pi}.$$ In experimental uncertainty, ${\Delta}x$ is actually half the range (since the value implies that the actual value ...
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1answer
267 views

Using the Metric in Book Gravitation (MTW)

Here is the whole Box 2.2, at Page 55 The dot behind the second $-p^2$ seems to be a "planck mass" (sarcasm, flea egg) or just the book's style to use Dot behind the equations. So the Equation is ...
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2answers
196 views

Where does $\pi$ come from in the Heisenberg equation?

In class today we were taught about Heisenberg’s equation, $$\Delta x\Delta p\ge\frac{h}{4\pi}. $$ Experience tells me that any time an equation involves pi, circles aren’t far behind. Obviously this ...
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2answers
169 views

Notation in Heisenberg Uncertainty Relation: greater than with tilde: $\gtrsim$

In "The Road to Reality" (pg. 523), Roger Penrose writes: Heisenberg's uncertainty relation tells us that the product of these spreads cannot be smaller than the order of Planck's constant, and ...
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3answers
97 views

If Heisenberg uncertainty principle involves the standard deviation of quantities then why do we use it in a different way as here?

Heisenberg uncertainty principle is mathematically given as $$\sigma_x \cdot \sigma_p \ge {{\hbar} \over {2}}$$ The two terms on the left being the standard deviations of position and momentum. But on ...
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3answers
66 views

Different definitions of the uncertainty principle

In the book Introduction to Quantum Mechanics by Griffiths, the mathematical form of the uncertainty principle is stated as $$\sigma_x \sigma_p \ge \frac{\hbar}{2}.$$ However, another book on QM, that ...