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A quantum particle moves in the potential (with μ > 0) μ(μ+1) ħ² V(x) = 2 m a² [cosh(x/a)]² (a) Find the scattering stat
Posted: Fri May 06, 2022 6:12 am
by answerhappygod
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A quantum particle moves in the potential (with μ > 0) μ(μ+1) ħ² V(x) = 2 m a² [cosh(x/a)]² (a) Find the scattering states for this problem as follows: First, set Pk (x) = eik ok(y) with appropriately chosen k and y = x/a. Next, substitute z = tanh y, and show that the resulting power series for Ok(z) terminates (only) if u is an integer. (b) For μ = 1, 2, determine the scattering states (E≥ 0) explicitly, and find the allowed bound states (E< 0) and their energies.