# Uncertainty time/frequency

• Gavroy
In summary, the user is looking for the correct equation to determine the linewidth based on the emission process time. They have found three equations online and are asking for clarification on when to use each one and if they are correct. The expert recommends defining the lifetime and linewidth precisely and provides an equation that takes both into account, stating that the width is equal to 1 over 2 pi times the lifetime. They also mention that the shape of the line is a Lorentzian and provide a formula for it.

#### Gavroy

hi

i am looking for the correct equation, that gives me the linewidth by knowing the time of the emission process.

so far, i found in the internet:

Δf=1/(Δt), Δf=1/(4πΔt) and Δf=1/(2Δt)

can you tell me, when i have to use which of these equations and maybe whether you think that these equations are correct?

sry for my english, still practising! ;-)

Gavroy, Getting the factor right requires saying precisely what you mean by the lifetime and the linewidth. A decaying state is described by a wavefunction |ψ|2 ~ exp(-Γt/ħ), so the lifetime of the state may be defined as Δτ = ħ/Γ.

The shape of the line is a Lorentzian, 1/((E-E0)2 + (Γ/2)2) which reaches its half-height at E = E0 ± Γ/2, so the "width" in that sense is ΔE = Γ. All right now ΔE = ħ Δω = 2π ħ Δf, so putting it all together you get Δf = 1/(2π Δτ).

## What is uncertainty time/frequency?

Uncertainty time/frequency refers to the inherent unpredictability or variability in the timing or frequency of a measurement or event. It is a measure of how much unknown information or error is present in a given measurement or calculation.

## Why is uncertainty time/frequency important in scientific research?

Uncertainty time/frequency is important in scientific research because it affects the accuracy and reliability of our results. If we do not take into account the uncertainty associated with our measurements, our conclusions may be flawed or misleading. Additionally, understanding and managing uncertainty allows us to make more informed decisions and better communicate our findings to others.

## How is uncertainty time/frequency calculated?

Uncertainty time/frequency is typically calculated using statistical methods based on repeated measurements or known sources of error. This can include techniques such as standard deviation, confidence intervals, or propagation of errors. The specific method used will depend on the type of data being analyzed and the level of uncertainty desired.

## What factors contribute to uncertainty time/frequency?

There are many factors that can contribute to uncertainty time/frequency, including limitations of measuring instruments, human error, environmental factors, and natural variability. It is important for scientists to identify and account for all potential sources of uncertainty in their research to ensure accurate and reliable results.

## How can uncertainty time/frequency be minimized?

Uncertainty time/frequency can be minimized by using more precise and accurate measuring instruments, reducing sources of error, and increasing the number of measurements taken. Additionally, incorporating advanced statistical techniques and accounting for all possible sources of uncertainty can help to minimize its impact. Collaborating with other researchers and conducting studies in controlled environments can also help to reduce uncertainty time/frequency.