referframe said: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?
As always, thanks in advance.
ZapperZ said: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.
No, a free particle cannot have a sharp energy. According to the Heisenberg uncertainty principle, the more precisely we know the position of a particle, the less precisely we know its momentum. Therefore, a free particle that has no forces acting on it cannot have a definite energy.
A free particle is a particle that is not acted upon by any external forces. It is not subject to any potential energy and therefore can move freely without any restrictions.
A free particle cannot have a sharp energy because of the uncertain nature of quantum mechanics. The position and momentum of a particle cannot be known simultaneously with 100% certainty, and therefore the energy of a free particle cannot be known with absolute precision.
No, a free particle cannot have a definite energy. As mentioned earlier, the Heisenberg uncertainty principle dictates that the position and momentum of a particle cannot be simultaneously known with absolute certainty. This means that the energy of a free particle can only be described in terms of a range of possible values.
The uncertainty principle states that the more precisely we know the position of a particle, the less precisely we know its momentum, and vice versa. This means that the energy of a free particle cannot be known with absolute certainty due to the uncertainty in position and momentum. Instead, it can only be described as a range of possible values.