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A particle is confined to move in one dimension in the region x ≥ 0 in a potential given by: U(x) = λx with λ=1eV/A. Assume the particle is in the lowest possible energy state.
(a) For a classical particle, what would be its position and its energy? Now assuming the particle is (i) an electron, and (ii) a proton, estimate using the uncertainty principle: (Hint: minimize the energy)
(b) What is the uncertainty in its position? Give your answer in A, for (i) and (ii).
(c) The particle's estimated kinetic energy, in eV, for (i) and (ii).
(d) Show that the ratio of its estimated kinetic energy to potential energy is independent of the particle's mass and of the value of λ. What is the value of this ratio? Smaller, equal or larger than 1? (Note: for the harmonic oscillator, the ratio is equal to 1).
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