The Hamiltonian of a particle of mass m is given by \(H=\frac{p^2}{2 m}+V(x)\), with
\(\mathrm{V}(x)=\left\{\begin{aligned} -α x & \text { for } x \leq 0 \\ β x & \text { for } x>0 \end{aligned}\right.\)
where α, β are positive constants. The nth energy eigenvalue En obtained using WKB approximation is
\(E_n^{3 / 2}=\frac{3}{2}\left(\frac{\hbar^2}{2 m}\right)^{1 / 2} \pi\left(n-\frac{1}{2}\right) f(α, β) \quad(n=1,2, \ldots .)\)
The function f(α, β) is
1
\(\sqrt{\frac{\alpha^2 \beta^2}{2\left(\alpha^2+\beta^2\right)}}\)
2
\(\frac{\alpha \beta}{\alpha+\beta}\)
3
\(\frac{\alpha+\beta}{4}\)
4
\(\frac{1}{2} \sqrt{\frac{\alpha^2+\beta^2}{2}}\)