Linked Questions
16 questions linked to/from Factor 2 in Heisenberg Uncertainty Principle: Which formula is correct?
1
vote
1
answer
4k
views
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 ...
- 283
4
votes
1
answer
622
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,
$$\Delta (x) \Delta(...
- 363
1
vote
1
answer
913
views
Heisenberg's uncertainty principle - Planck's (reduced) constant divided by $2$ or not? [duplicate]
The most common form of Heisenberg's uncertainty principle I've seen online is $$ \Delta x \Delta p ~\geq~ \dfrac{\hbar}{2}.$$
However, I also regularly see $$\Delta x \Delta p ~\geq~ \hbar. $$
...
- 455
0
votes
2
answers
1k
views
Why is uncertainty $\geq {\hbar}/{2} $ [duplicate]
Almost all uncertainties (for example the position-momentum uncertainty or time-energy uncertainty) are greater than ${\hbar}/{2} $. But what is the derivation of this uncertainty by Heisenberg? Is ...
- 2,489
3
votes
2
answers
202
views
Mathematical Expression of Heisenberg's Uncertainty Principle [duplicate]
In some situations the mathematical expression of the principle is $$\Delta x \Delta p \ge \hbar$$
But sometimes it is written as $$\Delta x \Delta p \ge \frac {\hbar}{2}$$
Why such a difference? And ...
- 39
1
vote
0
answers
57
views
Different statements of the Heisenberg's uncertainty principle [duplicate]
In different books, but also websites, there are different expressions for the Heisenberg's uncertainty principle. For example,
$\Delta x \Delta p \ge h$ (from The Physics of Atoms and Quanta)
$\...
- 33
0
votes
0
answers
55
views
Is the Uncertainty principle $ΔxΔp ≈ h$ an approximation? [duplicate]
The original paper by Heisenberg that discusses the Uncertainty principle has the following relation
ΔxΔp ≈ h
where x position, p momentum.
Meaning, you can't do better than Planck's constant in the ...
- 155
0
votes
0
answers
37
views
Explanation of Different factor of $2$ in Formulas for the Uncertainty Principle [duplicate]
I am readind about Heisenberg's Uncertainty Principle and although the main formula most texts use is
$$\Delta x\Delta p_{x}\geq \frac{\hbar}{2}$$
or equivalently
$$\Delta x\Delta p_{x}\geq \frac{h}...
- 495
3
votes
1
answer
8k
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 ...
- 1,550
2
votes
2
answers
835
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 ...
- 952
2
votes
3
answers
540
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 ...
- 1,290
2
votes
1
answer
1k
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 ...
user148792
0
votes
1
answer
386
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 ...
- 2,469
1
vote
2
answers
501
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 ...
- 159
0
votes
3
answers
146
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 ...
- 125