# Can Free Particle Have Sharp Energy?

Gold Member

## Main Question or Discussion Point

I read somewhere that a single particle traveling freely (not in a box, no PE function, etc.) cannot have a sharp energy. Is this correct? If so, why?

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dextercioby
Homework Helper
Where did you read that and what was the reasoning ?

ZapperZ
Staff Emeritus
I read somewhere that a single particle traveling freely (not in a box, no PE function, etc.) cannot have a sharp energy. Is this correct? If so, why?

We request that members who post something like this make exact reference to the source. This will force people, at least from now on, the pay attention to the source that they wish for us to address in the future.

This is a perfect example, because what you describe is actually false. A free particle that is described by a plane wave solution to the Schrodinger equation, will have a well-defined momentum. Since for a free particle, the momentum and energy operators commute with each other, it means that the energy of that particle is also well-defined. Thus, this is equivalent to having a sharp energy value at a particular value - a delta function.

So now we are left with the question on whether (i) you read your source correctly, (ii) you read a dubious, faulty piece of information, or (iii) a number of other possible explanations. Without knowing the source of the information, we have no way of knowing.

Zz.

Gold Member
We request that members who post something like this make exact reference to the source. This will force people, at least from now on, the pay attention to the source that they wish for us to address in the future.

This is a perfect example, because what you describe is actually false. A free particle that is described by a plane wave solution to the Schrodinger equation, will have a well-defined momentum. Since for a free particle, the momentum and energy operators commute with each other, it means that the energy of that particle is also well-defined. Thus, this is equivalent to having a sharp energy value at a particular value - a delta function.

So now we are left with the question on whether (i) you read your source correctly, (ii) you read a dubious, faulty piece of information, or (iii) a number of other possible explanations. Without knowing the source of the information, we have no way of knowing.

Zz.

I read it a couple of weeks ago. I will try to find the source. I think it was just somebody's paper that I ran into using Google. In any case, thanks for the clarification.