Problem 9.1 Use the WKB approximation to find the allowed energ... | Filo

SOLVED:An alternative derivation of the WKB formula (Equation 9.10 ) is based on an expansion in powers of ħ. Motivated by the free-particle wave function, ψ=A (±i p x / ħ), we write ψ(x)=e^i f(x) / ħ, where f(x) is some complex function. (Note that there is no loss of generality here- any nonzero function can be written in this way.) (a) Put this into Schrödinger's equation (in the form of Equation 9.1 ), and show that i ħf^''-(f^')^2 p^2=0. (b) Write f(x) as a power series in ħ: f(x)=f0(x) ħf1