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SamRoss
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Does a particle's diameter affect anything in determining its position, momentum, energy, etc.? Does it play any role in Shrodinger's equation?
Bill_K said:Introductory quantum mechanics deals with a single point particle that has no diameter.
Bill_K said:Elementary particles are, to our best knowledge, point particles. Only if you're dealing with an object that has internal structure, like a molecule, or an atomic nucleus, does this not apply. In such cases you may need to consider contributions to the energy from the internal degrees of freedom: rotation, vibration, or other modes of excitation.
The size of a particle does not have a direct impact on its behavior in quantum mechanics. Rather, it is the wave function of a particle that determines its behavior, and this is not dependent on the particle's size. However, the size of a particle can affect how it interacts with its environment and other particles, which can indirectly influence its behavior in quantum mechanics.
Yes, according to the principles of quantum mechanics, a particle can exhibit characteristics of both a wave and a particle at the same time. This is known as wave-particle duality and is a fundamental aspect of quantum mechanics.
In quantum mechanics, particles are described by their wave functions, which can extend infinitely in space. Therefore, there is technically no limit to how small a particle can be in quantum mechanics. However, at extremely small scales, the uncertainty principle dictates that the position and momentum of a particle cannot be known simultaneously, making it difficult to define the size of a particle at this scale.
The Heisenberg 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 as the size of a particle becomes smaller, its momentum becomes more uncertain, and vice versa. Therefore, the size of a particle is related to the uncertainty in its momentum, as described by the uncertainty principle.
Yes, the size of a particle can affect the probability of its location in quantum mechanics. This is because the wave function of a particle determines the probability of finding the particle at a certain location, and the size of the particle can influence the shape and behavior of its wave function. Therefore, the size of a particle can indirectly affect its probability of being located in a particular region of space.