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asdf1
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why is the height for the particle in a box expressed in eV and not in meters?
I've seen a lot of people get confused by this. When you see a graph for the potential of a 1-d box, keep in mind that its a 1-d problem. The particle only has an x-coordinate. The height represented is the magnitude of the potential energy. Likewise, when you see a graph for the wavefunction of a particle in a 1-d box, don't thing of this as showing the hieght of the particle versus the horizontal displacement. The particle does not have a hieght: it is a 1-d problem! The hieght represents the value of the wavefunction at the given displacement. This hieght squared is proportional to the probability of the particle being found in a small region around the point.asdf1 said:why is the height for the particle in a box expressed in eV and not in meters?
The concept of "Height for the particle in a box" refers to a theoretical model used in quantum mechanics to understand the behavior of a particle confined in a one-dimensional space. It assumes that the particle is confined within a potential well, creating a "box" with finite boundaries.
The height of the potential well determines the energy levels that the particle can occupy within the box. A higher potential well will result in higher energy levels, while a lower potential well will result in lower energy levels. This affects the probability of finding the particle at different positions within the box.
The particle in a box model is a simplified representation of more complex systems in quantum mechanics. It allows us to study the behavior of particles in a confined space and provides insights into important concepts such as energy levels, wave functions, and probability distributions.
The uncertainty principle states that it is impossible to know both the position and momentum of a particle with absolute certainty. In the case of a particle in a box, the height of the potential well determines the energy levels and, therefore, the momentum of the particle. This means that a higher potential well results in a more certain position but a less certain momentum, and vice versa.
In a theoretical sense, the height of the potential well can be changed to any desired value. However, in a real physical system, there are limitations and constraints that may prevent the potential well from being changed. For example, in the case of an electron in an atom, the potential well is determined by the properties of the atom and cannot be easily altered.