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Heisenberg Position-Momentum Uncertainty — result sheet
Calculate the minimum momentum uncertainty associated with a positive position uncertainty using the one-dimensional Heisenberg bound.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Minimum momentum uncertainty is Delta p_min = hbar / (2 Delta x), using hbar = 1.054571817e-34 J s; the corresponding minimum product is Delta x Delta p_min = hbar/2.
This calculator evaluates the lower-bound momentum uncertainty for an entered positive position uncertainty. It returns the minimum Delta p in kg m/s and the lower-bound uncertainty product in J s; it does not estimate a measured spread, instrument error, or a particular quantum state.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Position uncertainty (delta x) — m; Finite positive one-dimensional position uncertainty in metres.; minimum 1.0E-15; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Position uncertainty (delta x) | 1.0E-10 |
For Delta x = 1e-10 m, the minimum momentum uncertainty is 5.272859085e-25 kg m/s and the minimum product is 5.272859085e-35 J s.
Assumptions and limits
- Position uncertainty is a finite positive one-dimensional spread in metres and is interpreted as Delta x in the standard deviation form of the relation.
- The reduced Planck constant is fixed at hbar = 1.054571817e-34 J s, and the lower-bound relation is used without a state-specific covariance term.
- The equality value describes the smallest momentum uncertainty allowed by the stated bound; an actual state may have a larger product.
- Wave-packet shape, preparation, measurement apparatus, correlations, uncertainty propagation, and experimental safety are outside the calculation.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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