Uncertainly Concept& Relativity Theory


บางคนสงสัยว่าทำไม Uncertainly Concept จึงดูเหมือนมีหลายสมการ เพราะว่า
\hbar = \frac{h}{2 \pi}.
ซึี่งบอก h-bar นั่น คือ reduced Plank’s Constant ซึ่งบอกเมื่อความถี่เป็นหน่วยของ radian per second
นอกจากนี้ สมการไฮเซนเบิร์กยังมีการพัฒนาในช่วงแรก ซึ่งก่อเกิดสมการต่่างๆ ดังนี้
From the de Broglie relation, the size of the slit and the range in momentum of the diffracted wave are related by Heisenberg’s rule:
\Delta x \, \Delta p \approx h. \,

In his celebrated paper (1927), Heisenberg established this
expression as the minimum amount of unavoidable momentum disturbance
caused by any position measurement,[2]
but he did not give a precise definition for the uncertainties Δx and
Δp. Instead, he gave some plausible estimates in each case separately.
In his Chicago lecture[3] he refined his principle:

\Delta x \, \Delta p\gtrsim h\qquad\qquad\qquad (1)

But it was Kennard[4] in 1927 who first proved the modern inequality:

\sigma_x\sigma_p\ge\frac{\hbar}{2}\quad\qquad\qquad\qquad (2)

where \scriptstyle \hbar=h/2\pi, and σx, σp
are the standard deviations of position and momentum. Heisenberg
himself only proved relation (2) for the special case of Gaussian
states.[3] However, it should be noted that σx and Δx are not the same quantities. σx and σp
as defined in Kennard, are obtained by making repeated measurements of
position on an ensemble of systems and by making repeated measurements
of momentum on an ensemble of systems and calculating the standard
deviation of those measurements. The Kennard expression, therefore says
nothing about the simultaneous measurement of position and momentum.





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