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Consider a particle trapped in an infinite square well potential of length L. The energy states...

Consider a particle trapped in an infinite square well potential of length L. The energy states of such a particle are given by the formula: En=n^2ℏ^2π^2 /(2mL^2 ) where m is the mass of the particle.

(a)By considering the change in energy of the particle as the length of the well changes calculate the force required to contain the particle. [Hint: dE=Fdx]

(b)Consider the case of a hydrogen atom. This can be modeled as an electron trapped in an infinite well caused by the Coulomb attraction to the proton. By considering such a model in one dimension only, calculate the width of the well for an electron in the n=1 state.

(c) Compare this to the radius of a real ground state hydrogen atom. Are the results similar? State three assumptions made by the model that are not true in real life.

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