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Reflection-free potentials. A quantum particle moves in the potential (with μ > 0) µ(µ+1)ħ² V(x) = - 2ma² [cosh(x/a)]² (
Posted: Wed May 04, 2022 1:39 pm
by answerhappygod
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Reflection-free potentials. A quantum particle moves in the potential (with μ > 0) µ(µ+1)ħ² V(x) = - 2ma² [cosh(x/a)]² (a) Find the scattering states for this problem as follows: First, set Yk(x) = e¹k¹ ok(y) with appropriately chosen k and y = x/a. Next, substitute z = tanh y, and show that the resulting power series for (2) 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.