Uncertainty Principle and lifetime

[Niles]

Hi all

Please take a look here (just read the first paragraph): http://hyperphysics.phy-astr.gsu.edu/Hbase/quantum/parlif.html

I am a little uncertain of why it is that we equal the spread in time ∆t to the lifetime of the excited state (in the above link they denote the lifetime by Γ). What allows us to do this?

 

[Niles]

Ok, this explains it pretty well: http://en.wikipedia.org/wiki/Uncertainty_principle#Energy-time_uncertainty_principle

Thanks.

 

[Entropia]

The Uncertainty Principle states that it is impossible to know both the exact position and momentum of a quantum particle at the same time. This means that there will always be some uncertainty in our measurements of these properties. In the context of the link provided, this uncertainty is represented by the spread in time (∆t).

The reason we equate this spread in time to the lifetime of the excited state is because the excited state is a temporary state of the particle. It is not a stable state and will eventually decay back to its ground state. The lifetime of the excited state is the average time it takes for this decay to occur.

By equating the spread in time (∆t) to the lifetime of the excited state, we are essentially saying that the uncertainty in the particle's position and momentum is related to the time it takes for the particle to decay. This relationship is a fundamental aspect of quantum mechanics and is supported by experimental evidence.

In summary, the Uncertainty Principle and the lifetime of the excited state are connected because they both deal with the inherent uncertainty in the properties of quantum particles. The equating of the spread in time to the lifetime of the excited state is a result of this connection and is a fundamental aspect of quantum mechanics.