fundamenteel principe in de kwantummechanica
Ω = ω/2
. Note the tradeoff between the widths of the distributions.
Principe d'incertitude
princípio fundamental na física quântica
Inégalités mathématiques de la mécanique quantique
vertical
مبدأ الريبة
podstawowe prawo mechaniki kwantowej
квантова механіка
Necerteca principo de Heisenberg
Princip neurčitosti
불확정성 원리
mätosäkerhet inom kvantfysiken
Prinsip ketidakpastian Heisenberg
양자역학에서, 비가환인 두 관측가능량을 한꺼번에 정확히 측정할 수 없다는 원리
Werner Heisenbergin vuonna 1927 esittämä kvanttimekaniikan perusperiaate
Propagation of a de broglie wavepacket.svg
right
la principo, ke kvantuma stato ne povas havi kaj certan pozicion kaj certan movokvanton
fundamentale Relation der Quantenmechanik
量子力學概念
Proof of the Schrödinger uncertainty relation
Ω = 2ω
Uncertainty principle
Osäkerhetsprincipen
Heisenbergsche Unschärferelation
عدم قطعیت در تعیین سرعت یا مکان ذره
مبدأ التشكيك و عدم اليقين البَّاري الخاص بالتتربب الإلكتروني ( الإلكترونات )
What printing/edition does this page number refer to? Use year for that, and orig-year for original publication date
Αρχή της απροσδιοριστίας
Propagation of a de broglie plane wave.svg
Position and momentum probability densities for an initial Gaussian distribution. From top to bottom, the animations show the cases
osnovno načelo v kvantni fiziki
December 2024
量子力学における基礎的原理
不确定性原理
Heisenbergen ziurgabetasunaren printzipioa
Ω = ω
Relación de indeterminación de Heisenberg
principio fondamentale della meccanica quantistica
Предел точности измерения величин квантовой системы, открытый в 1927 году
, and
Zasada nieoznaczoności
কোয়ান্টাম বলবিজ্ঞানের এক মৌলিক নীতি
nguyên lý cơ học lượng tử
Принцип невизначеності
Principio de la mecánica cuántica
Propagation of de Broglie waves in 1d—real part of the complex amplitude is blue, imaginary part is green. The probability of finding the particle at a given point x is spread out like a waveform, there is no definite position of the particle. As the amplitude increases above zero the curvature reverses sign, so the amplitude begins to decrease again, and vice versa—the result is an alternating amplitude: a wave.
Prionsabal éiginnteachta Heisenberg
principi de la física quàntica
不確定性原理
Принцип неопределённости
Onzekerheidsrelatie van Heisenberg
Principi d'incertesa de Heisenberg
Principio di indeterminazione di Heisenberg
Fundamental principle in quantum physics
Princípio da incerteza de Heisenberg
The derivation shown here incorporates and builds off of those shown in Robertson, Schrödinger and standard textbooks such as Griffiths. For any Hermitian operator , based upon the definition of variance, we have we let and thus Similarly, for any other Hermitian operator in the same state for The product of the two deviations can thus be expressed as In order to relate the two vectors and , we use the Cauchy–Schwarz inequality which is defined as and thus Equation can be written as Since is in general a complex number, we use the fact that the modulus squared of any complex number is defined as , where is the complex conjugate of . The modulus squared can also be expressed as we let and and substitute these into the equation above to get The inner product is written out explicitly as and using the fact that and are Hermitian operators, we find Similarly it can be shown that Thus, we have and We now substitute the above two equations above back into Eq. and get Substituting the above into Equation we get the Schrödinger uncertainty relation This proof has an issue related to the domains of the operators involved. For the proof to make sense, the vector has to be in the domain of the unbounded operator , which is not always the case. In fact, the Robertson uncertainty relation is false if is an angle variable and is the derivative with respect to this variable. In this example, the commutator is a nonzero constant—just as in the Heisenberg uncertainty relation—and yet there are states where the product of the uncertainties is zero. This issue can be overcome by using a variational method for the proof, or by working with an exponentiated version of the canonical commutation relations. Note that in the general form of the Robertson–Schrödinger uncertainty relation, there is no need to assume that the operators and are self-adjoint operators. It suffices to assume that they are merely symmetric operators.