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phys2
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I was wondering why the spacing between energy values keep increasing for the infinite potential well?
The solution of the Schrödinger equation inside the square well is a plane wave identical to a free particle, but due to the boundary conditions only discrete levels n are allowed. The momentum p scales with n, i.e. p~n; the energy scales with p², so E=p²/2m~n².phys2 said:I was wondering why the spacing between energy values keep increasing for the infinite potential well?
An infinite potential well is a theoretical model used in quantum mechanics to describe the behavior of a particle confined within a certain region. It consists of infinitely high potential walls on either side, creating a finite space in which the particle can exist.
The energy values in an infinite potential well are determined by solving the Schrödinger equation, which is a mathematical equation that describes the behavior of quantum particles. The solutions to this equation give the allowed energy levels for the particle in the well.
The energy values in an infinite potential well represent the allowed states of the particle within the well. These energy levels are quantized, meaning they can only take on certain discrete values, and they play a crucial role in understanding the behavior of quantum particles in confined spaces.
The width of the well has a direct impact on the energy values for the particle inside. A wider well will have more allowed energy levels, while a narrower well will have fewer. The energy values also become closer together as the width of the well increases.
No, the energy values in an infinite potential well cannot be measured experimentally because it is a theoretical model. However, the predictions made by the model have been confirmed through experiments on real systems that exhibit similar behavior, such as electrons in a semiconductor crystal.