Zur Quantenmechanik einfacher Bewegungstypen.

Kennard, E. H. (1927). Zur Quantenmechanik einfacher Bewegungstypen. Zeitschrift für Physik, 44(4), 4-5.

Type

Journal article

Intellectual base

Primary research

Year

1927

Volume

44

Issue

4

Pages

4-5

DOI

10.1007/bf01391200

DOI registrant

Springer Nature

Link

https://doi.org/10.1007/BF01391200

Cited from

physics

Cited by

2 citations across 2 artifacts.

Each citation links to the sentence it supports in the citing article.

Primes

• Conjugate-Observable Complementarity
  • The precision-product bound is the inequality \(\Delta x \cdot \Delta p \geq \hbar/2\) — not two separate limits but a single floor on the product (the floor invariant), with the floor set by the canonical commutator \([\hat{x}, \hat{p}] = i\hbar\).

    This sourceProves the rigorous inequality Δx·Δp ≥ ħ/2 and characterizes minimum-uncertainty (saturating) Gaussian wavepackets.

    Supported in partVerified against the publisher's abstract

    Kennard's abstract confirms only that in these simple cases the quantum-classical difference reduces to Heisenberg's uncertainty relation between canonically conjugate variables; no inequality, constant or commutator appears.

    “Das Ergebnis kann dahin formuliert werden, daß der Unterschied der Quantentheorie von der klassischen in solchen einfachen Fällen nur in der Heisenbergschen Unbestimmtheitsrelation zwischen den Werten kanonisch konjugierter Variabein besteht.”

    Read by an automated reader; not a human review. How support was checked

Domain-specific

• Canonical commutation relation
  • … transfers from On suitable wavefunctions, x multiplies by position and p equals minus iℏ times differentiation, so xp-px equals iℏ. to A derivation states operator domains and boundary conditions and avoids treating unbounded operators as finite matrices, where the trace identity would contradict the relation..

Verification

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Registry ID ref:0e5531ddf5a1 · see in the full table