Prove that the energy state of a particle in a potential well of finite width and infinite depth are discrete, but they are not equispaced.
Answers
Explanation:
The finite potential well (also known as the finite square well) is a concept from quantum mechanics. It is an extension of the infinite potential well, in which a particle is confined to a "box", but one which has finite potential "walls". Unlike the infinite potential well, there is a probability associated with the particle being found outside the box. The quantum mechanical interpretation is unlike the classical interpretation, where if the total energy of the particle is less than the potential energy barrier of the walls it cannot be found outside the box. In the quantum interpretation, there is a non-zero probability of the particle being outside the box even when the energy of the particle is less than the potential energy barrier of the walls (cf quantum tunnelling
The energy state of a particle in a potential well of finite width and infinite depth is discrete
1) The finite potential well (also known as the finite square well) is a concept from quantum mechanics. It is an extension of the infinite potential well, in which a particle is confined to a "box", but one which has finite potential "walls".
2) Unlike the infinite potential well, there is a probability associated with the particle being found outside the box. Classically, this is perfectly logical to me.
3) If we confine a discrete particle to a small region in one-dimensional space, it makes sense that it would bounce around (against the walls of its confines), much more than if we were to confine it to a larger region in one-dimensional space.
4) The quantum mechanical interpretation is unlike the classical interpretation, where if the total energy of the particle is less than the potential energy barrier of the walls it cannot be found outside the box.
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